I’m no acoustics guy by any means but I’d think you’d want research the concept of floating the floor" (as I see it commonly referred to). My understanding is that if you want isolation, you want a dense, rigid material, an air gap, and another dense, rigid material below. The idea is you’re decoupling the fake/floated floor from the floor below to prevent vibrations, and the air gap between the two rigid surfaces should kill the bleed. To isolate a recording studio from outside noises, you’re encouraged to build a room within a room and float the floor, so this is a similar concept. In your case, you’ll probably be able to get away with an elevated platform versus the entire floor, but the decoupling part may be the challenge.
My totally amateur understanding is that low frequencies are the hardest to absorb, so if your neighbor is hearing the sub-frequency thump from your bass, playing directly on top of absorption materials (without an air gap) may not solve the problem as absorption materials may not reach those frequencies (unless you’re standing on a lot of them). Hence why I think the decoupled floor would be key. If you already have a large rubber pad, maybe try to DIY a small elevated platform on top of that with an air gap below (think: wide, shallow upside-down wood crate), and test with your neighbor to see if that does the trick. The trick would be to keep the platform smaller than the dimensions of your rubber pad so the edges of the platform are never directly touching the floor below. Maybe throw another rubber pad at the base where you’ll actually play on so you’ll have (from top to bottom): bass, rubber pad, elevated platform with air gap, rubber pad, floor.
Now, if the noise your neighbor is hearing isn’t just from the direct vibrations of the bass on the floor, that may not be effective enough. But the good news would be that type of approach may be inexpensive enough to build that if it doesn’t work, you’re only out a few bucks in lumber and some time. Whatever you do, I’d look to include the neighbor in the test phase “is it better now - if not how much worse?” I’d also try to hear for myself if I had anyone who could play notes on the double-bass while I stood in the neighbors room for a before/after. I mean, if I were down there and heard that the bass was pretty darn loud and wasn’t limited to sub frequencies, I’m not sure I’d even bother with this approach. If it was just a low-frequency thump, I’d give it a shot though.
Note: I’m not speaking from any direct first-hand experience. I’ve bought bass traps and broadband absorbers to improve the acoustics of a room, but never had to build an isolated space, which is something else entirely. I’ve read stuff on forums about the concepts at a high level and that’s the only reason I’m suggesting the decoupled floor approach. If I were in your situation, I’d try to start with an elevated platform because it may be the cheapest and easiest way to potentially get the right results, and if not, you’re only out a few bucks in lumber and time before looking into more expensive alternatives like trying broadband absorption or consulting pros.
Worst case: ask to switch apartments. 
Totally missed that one! I thought this was in reference to a speaker of some sort.