She has a wand, but it's unclear how she got it.
Bellatrix did get a wand after hers was stolen. It's unclear how exactly she got it, but it isn't mentioned as being anyone else's wand, like Narcissa's or Draco's. In the movie, we see her new wand, and it doesn't look anything like any of the Death Eaters' wands.
There are several ways she could have sourced herself a new wand.
She could have taken one from a victim of the Death Eaters (like Charity Burbage).
She could have taken one from a lower-ranking Death Eater, it would be more important that she had one than them.
Ollivander made Pettigrew a new wand, it's possible he was also forced to make spare wands as well, even if not specifically for her.
Another thing to remember is that once Ollivander was kidnapped, his shop was left empty. Even after he was freed from the Death Eaters, he was in hiding, and would have still left his shop empty. The Death Eaters could easily have looted it somehow for wands.
In addition, Harry mentioned that they left two wands at Malfoy Manor.
“We left your wand and the blackthorn wand at the Malfoys’, Hermione.” Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)
It's likely that using a different wand affected her dueling skills to some extent.
Dueling with an unsuitable wand certainly can have negative effects.
Harry wasn't able to use a Snatcher's blackthorn wand nearly as well as his own. He described it as making even his simple, minor spells less powerful and effective.
“Sorry – reducio.’
The spider did not shrink. Harry looked down at the blackthorn wand. Every minor spell he had cast with it so far that day had seemed less powerful than those he had produced with his phoenix wand. The new one felt intrusively unfamiliar, like having somebody else’s hand sewn to the end of his arm.” Harry Potter and the Deathly Hallows, Chapter 20 (Xenophilius Lovegood)
In addition, Hermione was barely able to stand having Bellatrix's wand, since it felt like a part of her.
“Hermione looked frightened that the wand might sting or bite her as she picked it up.
‘I hate this thing,’ she said in a low voice. ‘I really hate it. It feels all wrong, it doesn’t work properly for me … it’s like a bit of her.” Harry Potter and the Deathly Hallows, Chapter 26 (Gringotts)
Bellatrix could have also felt like the wand was a part of her, and for her that would be a benefit since it was so attuned to her. Ollivander says the relationship between a wizard and their wand is very important.
“The best results, however, must always come where there is the strongest affinity between wizard and wand. These connections are complex. An initial attraction, and then a mutual quest for experience, the wand learning from the wizard, the wizard from the wand.” Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)
Simply by having and using her wand for so long, Bellatrix's wand would have been more attuned and connected to her than a new one, even one perfectly suited to her, because she's had hers for longer and it's had time to "learn" from her.