sounds like great mix for worms. They would help work over the mix and add a boost to your compost. Take a look at the vermiculture site for more ideas if interested in going that route.

Compost happens. How well your system might work depends on whether your mix is fairly close to the 30 parts Carbon to 1 part Nitrogen as well as the moisture in the mix. Since mulch is any material that is layed on the soils surface and can be wood chips, shredded leaves, shredded bark, or even stones we cannot guess what you have with out a better description of your "mulch".

How big is your bin?
What is the 'mulch' material, shredded wood chips?
How large are the pieces? If it is like the large wood chips I got from a nearby yard having a tree taken down, they are not going to break down quickly.

Without more details I can't be sure, but it sounds like you may have to wait a few years for 'black gold'.