He banished Heimdall because Heimdall betrayed him.
I think you got it backwards. At first Loki tried to have Heimdall on his side. There is a scene in the film where Loki asks Heimdall whether Odin was afraid of him; Heimdall says he wasn't, because he knew he was loyal to him as his king. So Loki says: Well, now I'm your king, so you'll be loyal to me.
However, after that scene, Heimdall goes against Loki by sending Thor's four friends to midgard to help him come back (disobeying Loki's direct orders).
Seeing that Heimdall wasn't loyal to him, Loki relieved him of his duties and freezed him. Heimdall was already his enemy - he did not make an enemy out of him; he tried to have him on his side, but Heimdall did not want to be on his side.
It is only after this that he uses the bifrost in order to bring the Frost Giants to Asgard. At this point, it just didn't matter anymore whether he used it or not.
To summarize: he did not make an enemy out of Heimdall in order to use the bifrost; Heimdall was already his enemy, so he had to fight him, and then there was no reason not to use the bifrost.