There is a thread on Lonely Planet discussing exactly this topic. Which refers to 2 bus lines that offer service between Belize and Santa Helena/Flores/Tikal in Guatemala.
Express Buses – Flores / Belize / Chetumal
Two Guatemalan bus companies, San Juan Express Bus Service and Linea Dorada, provide bus service between Flores, Belize City and Chetumal; they do not make any other scheduled stops in Belize. In Belize City, buses arrive at and depart from the Belize City Water Taxi / Marine Terminal on North Front Street near the Swing Bridge. Buses operate on Sundays and public holidays. Not all buses are air-conditioned. The schedule below was in effect on 20 December 2007 but always confirm times before travel.
The thread is from back in 2008 so information is a bit dated but I was able to find the companies Linea Dorada seem to offer a stop in Belize but on only one of its routes and it may not work for you timewise, the other seems to be discussed at length on Tripadvisor and not under the best of terms.
There is a sort of 3rd party information site information on which I can't verify but it gives you some contact information for both companies listed above so you can check prices and schedules as needed.
One other company that is mentioned in the TripAdvisor article is Adrenalina Tours, which actually does offer a shuttle from Belize to Flores for $28 the only thing is I can't seem to find the schedule of when it leaves Belize but you can try contacting them to check.