Bellatrix wins this duel with ease. She has better dueling feats than any other character with the exceptions of Dumbledore, Voldemort and Grindelwald. She is far and away the strongest witch in the modern Potterverse as far as dueling is concerned. She defeated Kingsley Shacklebolt in seconds, deflected an attack from Albus Dumbledore (something only She, Voldemort and Grindelwald have done) while he was weidling the elder wand, she completely roflstomped a room full of snatchers including Fenrir Greyback, killed Sirius Black, beat Nympahadora Tonks (who she'd later also kill) and beat Kingsley Shacklebolt all in the span of a few minutes fighting, and she's duelled 3 notable opponents at once... and was winning... a feat she shares with Voldemort. It's also worth nothing that she was an incredibly skilled Occlumens (enough so that she trained Draco to such a level he could resist Legilimency from Severus Snape) and a "prodigious" witch in general. Only witch in the modern Potterverse who even stands a chance in a duel with Bellatrix is Minerva McGonagall. She wasn't Voldemorts right hand woman and "best lieutenant" for no reason.

Also this fight happened once before... Bellatrix fought Hermione, Luna and Ginny all at the same time 1 v 3... and Bellatrix won (nearly killed Ginny forcing Molly Weasley to intervene, ending the duel with the trio in a victory. Had the duel gone on uninterrupted it's clear that Bellatrix would've easily mopped up her remaining two opponents. From the way Harry describes it in the novel, even before Ginny was nearly killed it looked like the 3 needed help and were being overpowered by Bellatrix).

Bellatrix wins this with ease. She'd probably have plenty of fun doing it too... She'd be able to afford to spend some time "playing with her food" as Dumbledore put it. It would be a slow end for Hermione. Bellatrix wins :)