Leaving your DNA on your bar, as opposed to their bar (whether or not you actually scrape your shins or not, just tell them).
Same thing with chalk, even though they allow it, "messy" chalk on your bar, not theirs. idk.
Uhhh, I got nothing else. ¯\_(ツ)_/¯ Good luck, and I don't see why it would be a problem.
Only thing is, where to store it/lock it up at their facility, so it doesn't get used for rack pulls,
or some person is in the middle of benching with it when you show up to lift.
(and you actually have to wait to use your own bar, sad).
The gym owner may not want to responsible for your bar in their gym.
Damage/theft. You may have to sign, or offer up a waiver or some sort.
I might have to go this route at my current gym.