Using a sub with no sub out on my amp

You are going to need a powered subwoofer. You run your speaker cables into it, set your filter, then run another set of speaker cables out of it and into your speakers.

So running my speaker cables out of the back of my amp into the sub is not going to change the sound that I'm getting out of my speakers is it going to alter the sound in any way obviously other than adding bass through the sub ?

You can also just run leads from the speaker to the sub. It won’t effect your sound unless you are a bat with super hearing. 
Not all subs take this type of connection. Rel is a brand that does. 

Id save more money,250 isnt going to get you anything worth buying .Get a used Rel t5i and run it high level output off your speaker outs

Thanks guys for the replies I'll look into that suggestion see what I can find one for.  Either that or I just look for another amp.

Your amp is fine. 2 options- buy a sub with speaker level inputs, or add a Line Out Converter to run a sub at line level off your speaker terminals. Either way no changes to the amp and won't affect the amp.

A LOC is just a couple 10k to 20k resistors that drops speaker output down to line level. They are under $20 at Parts Express, or you can even DIY for only about $2. That's what I did, see the pic on my system page. https://systems.audiogon.com/systems/8367?utm_campaign=website&utm_source=sendgrid&utm_mediu... If its good enough for me....  
With subs don't bother spending a lot on one it is better to use more, but one is better than none- 2 is better than 1, etc.

Don't worry about which channel either. Seriously, I have done it all these different ways, adding subs to an amp with no sub out is the easiest thing you can do.

Luckily, it’s not the amp, it is the speakers that are lacking in bass. Any self-powered sub with speaker wires in/speaker wires out will solve your problem.

I just added this 800 wpc self-powered sub to my small office system.

https://www.rockvilleaudio.com/rock-shaker-12-wood/

On sale, in your budget, 90 day trial with free return shipping (I bet you keep it like I did).

It gives a nice fullness to my bookshelf speakers. Don’t over-do it, just a bit, un-noticeable until you turn it off.

Your speakers are 89 db sensitivity (better than my Wharfedale Diamond 225 87 db)
Your amp is 30 wpc, more than my Luxman’s 10 wpc.

Your woofers are 5-1/8" diameter, they can be great but can only move so much air. Mine are 6-1/2", same thing.

When your sub’s amp takes the low bass job away, the bookshelf speakers then do a better job with upper bass/mids/highs and thus imaging improves along with detail ... no distortion from trying to do what they cannot do.

You will be happier at lower volumes after you add a sub to those speakers I bet.

Prior response, add single sub, I assumed a space without a lot of space like my small office.

IF you have the space for placement, and listening position to enjoy imaging, bass and the overtones of the bass notes give directionality and stereo imaging.

You might want to try a stereo pair of subs. These are ideal for that, front firing, no port. Place l/r adjacent to your mains.

Easy to try, Rockville will let you return the second one if you find it’s not worthwhile in your space.

If you go for a pair, perhaps their 10", or even their 8" will do, scroll down on the same page as above

https://www.rockvilleaudio.com/rock-shaker-12-wood/

you know your space and budget. You can give them some info and ask their advice.

I just checked, the 12" has no Port (my preference and advice). The 10" and 8" models have a rear port. If not near corners ok, but avoid them if possible to achieve the kind of imaging the pair is intended to achieve. Single sub, a port can get 'more' but I find it's risky, you can get 'more' mud.

Thanks for everybody's replies I appreciate it.  First let me say that when I hook up my Cambridge audio axr 85 amp to my speakers there is plenty of bass I'm not a base head so I'm not looking to get crazy amounts of Base but when I hook up my Cambridge to those speakers there is enough I'm satisfied with the bass I just don't like the rest of the sound signature.

I'm not sure if my speakers because why am I getting good bass out of a different amp but when I hook it up to my IO amp I'm not getting as good a base I think it's the amp and I know I'm not going to get really great bass out of a 5 inch woofer.

Those wharfedale diamond 225s I've always wanted those and I heard that those pair very well with my rega IO.  It does have a bigger woofer in The wharf tales and it's not that much bigger of a speaker than mine dimension Wise it's not a whole lot bigger it's a half inch wider 2 in taller I've read a lot of stuff around the internet and on these forums about the wharf deals with my amp 

But I do like to sound signature with my speakers there's just not enough face so I'll probably just add a subwoofer I don't want to sell my speakers get the wharf tales I don't like them.  I'm definitely going to check into your guys recommendations for subwoofers wasn't planning on having to buy one so I really don't have much of a budget for one.

My room is 10 ft x 12 ft so it's not very big and my speakers sit on my desk they're about 5 ft apart I got them on stands so it's not an absolute ideal situation where I can pull them out into the room and put them on floor sanders and probably get how much improve sound with my current room I just don't I can't pull it off they have to go on the desktop.  I will say though they do sound good on the desktop the image well they sound good I got them towed slightly in I'm just missing the low end punch.

I wouldn’t put too much stock in wharf tales if I were you. Fishermen always brag about the one that got away.

Well its kinda a know fact the Wharfdales 225 pair well with Rega IO, at least everywhere i read.

Im going the sub route.

Problem is my small budget of $250.  I want a small footprint also, im guessing 10 inch sub is plenty for my size room.  Looking for suggestion on brands and models in my price range, probally not alot of options, i just dont have anymore budget to go higher.

Strange that the amps sound SO different in the same space and same speakers. Is there an impedance mismatch somehow, phase reversal, .... ?

Speakers on your desk. IF you spend a good deal of time in your office, have you considered changing everything in there? I’m retired a few years already, finally weeded unneeded stuff from when I ran my business from here, and accumulated stuff. That opened up possibilities.

Our rooms are similar, mines essentially 11’ x 11’ room, difference is I pulled my desk back away from the front wall (wharfedales ear level inside bookcase opposite), got myself/monitor/keyboard dead center. Whoopee.

Cutting the bookcases down to 3 shelves high and putting a slightly larger top on them made a huge difference.

You can see my office system (or anyone’s system) like this:

Click on their user name. Click on Details. If a system is shown, click on it.

This one should fit the bill!
https://www.parts-express.com/Dayton-Audio-SUB-1000-10-100-Watt-Powered-Subwoofer-300-628
Or this!
Dayton Audio SUB-1200 12" 120 Watt Powered Subwoofer (parts-express.com)

No i have no choice but to put speakers on desktop on small stands, i just have no room.  My setup is in a bedroom, so very very limited ways to setup, desktop seems to be best.  If i pulled the speakers out off the wall and into the room it would open things up im sure, just dont have the space.

Those dayton audio look good, has very good reviews on parts Express also great video on how to hook it all up and tune it in excellent thank you.