You're not bi-wiring if the jumpers are connected. You need two two-conductor cables per speaker. The first two-conductor cable goes to the HF posts of speaker number one. The second two-conductor cable goes to the LF posts of speaker number one. Repeat for speaker number two with two more speaker cables. The jumpers between the HF and LF posts are removed.
Now there's the amp end to worry about. You have four conductors (i.e. two two-conductor speaker cables) for each speaker.
If your amp has two pairs of speaker outputs per speaker(i.e. two black and two red per speaker), then the two conductors in each the two speaker cables per speaker (i.e. four conductors in total) all have a place to plug in to.
If your amp only has one pair of speaker outputs per speaker (i.e. one black and one red per speaker), then what do you do with only two amp outputs per speaker but four wires per speaker? ...You have to strip the ends of the speaker cables and crimp or solder the two speaker cables together, (i.e. red to red and black to black) Now you can terminate with a single banana plug (or spade) and plug into the amp as if it were a single speaker cable.
The purpose of bi-wiring is to minimize the interaction between HF and LF by separating them as much as possible. That's why the jumpers between the HF and LF binding posts are removed and why two cables are used.
The HF and LF signals are still mixed at the amp end of course (unless you are using an active crossover). The question is then asked: "How do the HF and LF frequencies "know" which wire to take?" The answer is they don't "know" anything. If you pour a bucket of water on a hill, how does the water "know" it should go downhill rather than uphill? It doesn't "know" anything. It simply chooses the path of least resistance, i.e. downhill. Similarly, the signal simply chooses the path of least resistance. The signal coming from the amp "sees" a wire with a high pass filter in the speaker crossover and a wire with a low pass filter in the speaker crossover. It simply "chooses" the wire that is easier to travel down. It's not a perfect separation since the speaker crossover is not perfect. That's why active crossovers are better, because you get a precise separation. However, if you have the right system, bi-wiring can produce a noticeable benefit.