Many years ago when oil based paint was still readily available and common (at least in CA) we used it to paint the kitchen and bathroom. I threw a bunch of paint and paint thinner soaked rags into the trash can outside (plastic, hot summer day). My dad came home from work and he almost shit a brick when he saw me throwing in the last of the rags and other painting supplies into the trash. Yelled at me good, demanded I pick all of them out of the trash, and turned the hose on the trash can to soak the rest of the stuff in water. To say he was pissed was an understatement. I don't think he slept well that night worrying about the trash bursting into flames.
Of course, I knew I shouldn't have done any of that but was just being lazy. After that, I now always lay oily rags of any kind on the driveway to dry out overnight and throw them out when they're dry and crusty.
OP- BLO will have an odor for a good while as it dries and cures. It might suck in an apartment. Might want to try shellac. It's alcohol based and dries fast, doesn't really smell, and is non toxic when dry. You can get it in cans to brush and spray cans also. If you're feeling ambitious you can even make your own with denatured alcohol and shellac flakes. There's a clear and amber shellac, the amber will give the wood the "warm glow" that oil does.