I traveled to Belize on my world trip through Latin America:
1. Shuttle from Flores (Guatemala) to Belize City and by ferry to Caye Caulker.
2. Ferry from Caye Caulker to Belize City and then the chicken bus to the border of Mexico. After stamping out in Belize we took a Tucktuck to the border of Mexico. This piece can also be walked in about 15 minutes, but we did not know exactly where since there were several roads. After stamping in, we took a taxi to the ADO bus stop in Chetumal. There is also a bus from the border to Chetumal, but it goes to the city center and not close to the ADO bus stop. We wanted to pay the taxi driver with USD. He offered only a bad exchange rate and we withdraw money from the ATM at the bus station and paid the taxi with pesos.
Belize is the only country in Central America where English is spoken.
Belize is not particularly cheap and everything costs about twice as much as in Guatemala or Honduras.
From Belize City to Guatemala operate bus companies like FDN that go at least to Flores. There is a good overview on Rome2Rio.
From Belize City to Mexico operate bus companies like ADO that go at least to Tulum and Cancun. There is a good overview on Rome2Rio. There is also a shuttle from the ferry terminals to Chetumal in Mexico.
Between the cities
The public buses are former American school buses and are called chicken buses because the locals sometimes take living chickens with them.