Yeah, he might have hated Bellatrix than more than Voldemort himself. Point is Bellatrix is the most devoted Death Eater.... We can even state that she was in love with him. Actually she is the mother of Voldemort's daughter, Delphini a.k.a. Delphi (it is believed Bellatrix must have become pregnant near the end of the 6th school year. Contrary to the movies, Bellatrix was in the book NOT present when Dumbledore was killed, and was therefore also not the one who conjured the dark mark after that. It is believed this was because she was pregnant at the the time or even about to give birth to Delphi). Delphi's existence is revealed in "Harry Potter and the Cursed Child". Point is, that Snape turning on Bellatrix, might have gotten him in disfavor with Voldemort himself. Although Voldemort was never in love with her (as he wasn't capable of love), he did appreciate her devotion to his course. If I remember correctly he also didn't take her death by Molly's hands lightly. And thus Snape's role would also be a bit awkward at best in that scenario. Of course, Bellatrix already suspected Snape of being a mole for Dumbledore (although she didn't live to see her suspicions confirmed), but mere distrust and pure loathing.... It's hard to predict how things would have gone.