It depends on when you arrive in Cancun but you'll probably need to spend the night in Chetumal. You can get there by bus for around $25US. You can then bus to Belize City, change buses and head for Benque.
We recently stayed at Hotel Marlon in Chet for the same price as noted above, decent value and close to food and clubs and about 10 minutes taxi from the bus station.
Look up ADO bus schedules at http://www.adogl.com.mx/home.asp?acc=refresh
I don't have a source for the Belize schedule. I think you pretty much just have to show up and take what you get.