First are the largest down there, they have mostly cross-city routes utilising articulated Citaros plus mostly Eclipse Solar and Geminis.
Transdev have several routes too, mostly operated by Optare Solos (I think?) but they also run the Coastliner from Scarborough to Leeds.

Arriva have a couple of routes, one of which being the 26 utilising Solo SRs.
EYMS run the X46 to Market Weighton where I imagine there's connections to Hull, this I think mostly uses Gemini 2s.