I too find it easier to deal with BZ $, rather than US $. Generally, I have some BZ $ with me from the previous trip, regardless, there are US $ in the stash that need to be converted as I go. I do my best to get these US bills converted quickly. Generally, having a few drinks and paying as I go gets the conversion started in a happy way.
After I run out of both BZ $ and US $, I go to the ATM on a semi-regular schedule until it is time to return to the land of milk & honey . . erm, I mean ice and snow, where I earn the $ so that I can blow it all in Belize.
azbob, you may be getting US $ change when you give over US $, but it has been my experience that rarely get US $ in change unless specifically requested, because I am on short time. Once in a while, the change will come with a US dollar or two, but only because they didn't have the right change in BZ $.