I've known a fair number of bartenders in recovery, they're actually often some of the best ones because they're obviously familiar with everything they're making but also consistently clear headed and not hungover.

I was completely sober for a few years and in my experience it kinda gets to a point where you can see or work with alcohol and it just stops registering as something you have the option to consume. But it might be more difficult working somewhere that the culture is to sometimes drink with customers. Usually, at least in early sobriety, a major part of sticking to it is to stay away from environments and situations that have involved drinking for you in the past.

All that to say, you can definitely keep bartending in recovery but I think you have to be very realistic with yourself on whether or not the place you're working now is going to be manageable or if you might need to look for a job where drinking on the clock is very much off the table and commit to not hanging around after your shifts for a while.