My girl Linda again. Tikal is the BOMB. I mean seriously it will blow your mind.
Bugs in the jungle won't give you half the trouble of the sand fleas on the cayes. Rat bastards! They will eat you alive. Use Deet (REI Jungle Juice is 100%). Also lavender oil (dab in your hair), B12 (in supplement or raw papaya), and garlic help repel mosquitoes and fleas.
Bugs in your room I highly doubt. You can also bring a mosquitoe net to drape around your bedding.
Anyway, they are part of the natural wonders of the land. You will encounter bugs along your journey, you just don't see at home. The ants there are really tiny for example. Bugs the mind!