Best way to visit Mt Bromo from Yogyakarta on the way to Bali?

We’ll be staying in Yogyakarta and want to visit Mt Bromo before heading to Bali. We don’t have a lot of time so trying to be as efficient as possible.

So far looks like we can fly from Yogya to Surabaya and then hire a driver to Mt Bromo (Ideally to see the sunrise). My question is more for the return, i.e. how I get from Mt Bromo to Bali and where I can leave my luggage while I’m at Bromo??