You are right that Billy is there to warn someone about Edward and the Cullens, but they are there to warn Charlie about Bella spending time with Edward. They did not come to warn Bella.
"He came to warn Charlie?" I guessed, more horrified than angry.
Edward just nodded, answering Billy's gaze through the rain with narrowed eyes." (pg 349)
Bella lies to Billy about where Charlie is because she doesn't want Billy to talk to Charlie before she has a chance to talk to him. She doesn't want Billy to "warn Charlie" about the Cullens so she is trying to keep them from talking. If she tells Billy that she doesn't know where Charlie is or how long he will be she is hoping Billy and Jacob will leave and not wait for him.