You can sue for every day you can't have enjoyment of your property. You would have to prove it with dates and times and if possible noise readings. But if it is so bad that it is ruining your sleep... maybe it is worth it.
If are renting you can go after a proportion of your rent. If you own, you would have to come up with a value for damages. If you get together a few neighbors, it can cost them so much they won't want to continue. Even if they are judgement immune, you could go after the bike itself. Getting it sold at auction to pay for the judgements. Or you can ask for abatement, basically an order to have the person stop disturbing the peace.
Also will depend on what is reasonable amounts of noise and what time it occurs. 80db noise at 3am in the suburbs is outside of normal, but could be normal in a busy downtown. If it is loud at 3pm, it will be much harder to convince anyone it is unreasonable.