What is the best way to ask for more responsibility at work?

Right now I have a few, well-defined duties at work (wine shop/wine bar). I’ve recently taken on more responsibility when the last manager found a full-time teaching job, so now I’m handling marketing and setting up wine tastings. There are a lot of things that need to be done around the store which nobody has taken care of in ages (or ever?). And these are things I know how to because of my past management experience.

The only problem is that I’m still a part-time employee, so I barely have time to handle my own responsibilities, never mind taking on more jobs. If I take on more hours, I’d need to bump someone else off the schedule or persuade the owner to spend more on payroll so that I could work longer. He’s also very busy (he has a full-time job outside of running this business), so we barely work together and rarely have time to talk.

Maybe it seems like I’m chomping at the bit, but it seems like there’s a clear opportunity here. Nobody else wants to/ can/ will do any of these things, and it could be great experience and a resume builder for me. I could also build revenue for the business- it’s a win-win, right?

I think what I need to do is schedule a meeting with the owner and make a clear, logical argument. Am I getting ahead of myself here? What’s the best way to go about this?