Your bass is allowed in the overhead bin if there is space available when you board, and if it fits.
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A bass and/or flight case likely wouldn't fit in a smaller aircraft. But the aircraft type is generally published on the airline website/app as part of the flight information, and search engines or AI can help figure out the specific overhead bin length for that combination of plane and airline.
The key is you would probably need to be in an early boarding group. For United that means boarding group 1, with group 2 being a long shot. Boarding group 1 with United is actually the 6th group of people that gets to board, but the 5 "preboarding" groups are generally not large (unless you're flying out of a United hub city and then there are probably a lot of Global Services and 1K passengers. but I digress...)
The other key is to have a flight case that would fit into the overhead bin of the specific aircraft you are flying, because you might not get the bin space or the flight attendants and pilots might not know the rules, even if you print them out in advance. So even the best laid plans might wind up with a checked bass...
But ... most airline people are really cool about things if you are too. So, if you bring the bass on board and they won't let you put it in the overhead bins, then it's very likely they will gate check the bass at no charge. At least for me. Cause I'm nice and friendly.