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When my daughter wanted to be rocked to sleep I used to sit on the edge of the bed and lean back slightly and that never hurt my back. But when I was ready to stop bouncing and rocking to sleep I used to lie down next to her to put her to sleep (she was around 18 months at the time, so this may not work for a younger baby). Babies are stubborn, my little boy flat out refuses to be put to bed any other way but with a breastfeed (was hoping to have been well and truly weaned by now😅) my daughter was a lot more accepting of a change in settling technique, I think a lot depends on their temperaments. If you want to change you just have to try, they might protest the first few nights, but they'll adapt eventually
Mine reached a point where bouncing no longer worked. I think it was after around 5 months but looking back, it's hard to say; I just realized I hadn't been doing it anymore. I kept trying the rocker, which she initially hated at bedtime (she liked to be up and moving), and eventually it took. Now I can get her down in a few minutes just calmly rocking and singing. I think maybe the singing helps because the key seems to be building other sleep associations and cues, other than just the bouncing. Now she knows that when she gets a paci, the light goes off, the white noise goes on, and I rock and sing to her, that it's sleep time.
You can habit stack and end bouncing. So do bouncing and something else (eg: bum patting or back rubs) and slowly over a few weeks reduce the bouncing. I stopped rocking my son to sleep at like 10 weeks with this method. It doesn't cause any tears or upset because it's slow and you introduce a comfort that isn't as taxing on your body.