Depends on the pre-amp that's in there but they usually last a fair while so long as you remember to unplug the cable when you're not playing. I never really play active basses any more but I used to gig with one all the time & rarely had battery issues.
Very cheap Anderton's own brand (I think) thing: https://www.andertons.co.uk/eastcoast-basses/eastcoast-mb4-bass-pearl-white
Figured if I buy it, decide it's not for me and sell it on it won't be a significant loss.
My only concern was the active pickup battery life but apparently they're normally good for 100's of hours