As far as I can remember, Ursa never used any kind of bending in the comics, nor was it implied that she could do such a thing. However, she did carry some "bending genes", as seen in the The Search and Smoke and Shadow comic, where
she had a third child, Kiyi, with the "commoner" Ikem (who's definitely not a firebender - he was attacked by firebenders and fought with swords). Kiyi was revealed in the third issue of Smoke and Shadow to be a firebender.
Obviously Zuko and Azula were benders too, but you could have argued that Ozai was a bender to begin with, so that could have stemed from here.
As the other answer mentions, though, obviously not all Avatar descendants are granted to be benders.