The correct term is bullir, with ll. It means stirring a liquid by the heat. Boil, move, shake the water particles, forming bubbles by heat. It is also a pressing movement of a lot of animals.
In Mexico it is used as to rush, riot to do something. The origin is doubtful, it can be a variant of the verb bullir in its meaning of "shake". It is very common to vulgarize your inflections 'buya' or 'buyas' by 'buiga' or 'buigas', as is the case with 'haya' by haiga.