just call. it'll be the easiest thing and you can ask them about stowing it in the overhead compartment or the other cabin stow.
i've flown with gear a lot (full band with keyboards, guitars, basses) and the band has never had any problems getting things through, but we thoroughly checked out the restrictions, etc. before ever trying it. since it's a domestic flight it probably won't be so bad, but there may be length restrictions you need to be aware of because if you can't fit your bass or it's too big for their limits, they'll put it in cargo and if you don't want it in cargo you'll need to either find another way to get it there or buy it a seat.