That's a topic near & dear to my heart. In my bass-playing career, I've struggled between always hearing "YOU CAN'T TEACH FEEL" and the fact that my first and most important instructor showed me an exercise that turned out to put me on the right path. My sense of timing was awful - I mean TERRIBLE. He'd set up a cowbell tone on the drum machine, and when I tried to hit the notes right on the head with my bass at, say, 80 bpm or something, he'd end up telling me "my overall was passable, but my individual notes were all over the map".
So he finally came up with this - we sat in his studio with the lights out, and only a single candle illuminating the room. He'd sit across from me while I had my bass in hand while seated. The drum machine was set for 80 (or was it 72? to emulate the human heartbeat). He'd have me try to hit the notes right on top of the head - for like 20 minutes. After a while it got hypnotic, especially with the single candle thing going on.
Once I started eliminating the "over-thinking" from the equation (I think it took me almost a half hour - I can't remember; it was a long time ago) and moving into "animal heartbeat" state of mind, then he told me to start ignoring the 2, 3, 4, 5, 6, 7, and 8 beats and just come down (with a bass note - any bass note) on the 1. The drum machine was set to play the 1 noticeably louder than the rest of the beats... so he just had me come down on the 1, and drop out until it was time for the 1 again. That set up a lot of silence on my part except for the drum machine - but the previous half hour of hitting all 8 beats had put me in such a self-hypnotic state that the hypnotic thing kind of persisted when he asked me to ONLY play on the drum machine's "beat #1". So instead of "anxious anticipation" waiting for the 1 to come around again, I started internalizing the subdivisions into something palpable and tangible - I was actually starting to feel it instead of "trying too hard". After a while I found that I could just calm down and quit anticipating anxiously, and just play the 1 bass note at the right time.
Mind you, I probably wasn't very good at the time, but my instructor's exercise set up a whole new thing inside me that wasn't there before. Now, 25 or more years later, I think I'm starting to get it pretty good.
But playing behind the beat is also a "feel" thing, and I find although it's not impossible for me, I don't think I'm very good at it. Maybe I need to find a funk band!