At Bristol:
All ramp activities are handled by Servisair/GlobeGround for all carriers, including BA.
But as far as the PAX handling side of things goes:
BA Citiexpress handle themselves as well as SN Brussels, Aer Lingus, Air Southwest and Eastern Airways.
Servisair/GlobeGround handle everyone else. There is a dedicated pax handling team for easyJet.
Regards