I can't advise re: how to frame it in your application, but I do know three MD's who had substance use problems during undergrad/med school/residency and I've done some work with people with co-occurring mental illness and substance use disorders.
- One had to take a LOA during residency to go to inpatient treatment for alcohol use and has now been sober for a few years but has to do UA's every month as part of a 5-year monitoring program
- One left residency/clinical practice after some legal issues related to alcohol use and now does non-clinical work and has been sober for a number of years
- One had ALL kinds of problems (including risky behaviors, stealing drugs, etc) and lost their license, went to jail, and can never practice medicine again
I don't know the third well at all (just met in passing while I was doing a training for a residential treatment facility in which the person was residing as part of their sentencing), but I can say that one of the others is completely burned out and feels like residency was an awful experience, even without having a mental illness. I follow some people on twitter who are open about their experiences with mental illness in the medical profession and seem to be doing well. It's not impossible, but it does sound very hard.
If you can get to a few years of stability and sobriety and have a really solid support system and understanding of yourself, I'm sure it's possible. If you're really strongly interested in medicine, I'd say just do the postbacc and see how you do. You may be able to find a mentor who is a physician in recovery/or diagnosed bipolar if you put yourself out there by asking around. There are special AA groups for medical professionals (caduceus groups) and other resources for physician wellbeing. Someone who has been through it directly would be the best to talk to, IMHO.