Our first few trips down, we just used US currency, as all places take it. However, a friend pointed out to me that if you exchange it, you actually get more Belize money than two-to-one.
Now we always go to Milo's on Middle Street and exchange it when we get there. So when we exchange, say, $500 US, we don't just get $1000 BZ, but more like $1030 plus or minus, depending on what the exchange rate is on that particular day. When we were down in January, it was lower than when we were there the time before, so it does fluctuate.
That may not seem like much, but hey, it will buy you an extra meal.
It also makes it much easier to figure change, tips, etc., especially when you pay in US and get change back in BZ.