Is There A Device For Home Use That Can Measure How Low The Bass In My Speakers Is?

For any measurement to be meaningful, you will need a pink noise source and a precision sound pressure level meter with a calibrated microphone.  You might be able to download a 1/3 octave pink noise source which you can burn to a CD.  Records or prerecorded tapes will of course be influenced by the frequency response of your cartridge and tape machine, which at very low frequencies could add another variable.  Where you place the SPL meter and what weighting filter you use will also affect your results.  Are you trying to measure just the speakers or the total response of your speakers in your listening environment?  Bruel & Kjaer wrote much on acoustic measurement and have published many books and booklets on making meaningful SPL measurements which I would highly recommend as useful reading.  Even the instruction book for their 2203 Precision Sound Level Meter has useful information for doing what you want to accomplish.