There are several actors who are known for doing their own stunts. Generally speaking, is it an industry convention to pay actors "bonuses" for performing their own stunts?
No, actors do not get paid extra to do their own stunts. Some actors enjoy the challenge of doing the stuntwork, while others feel it adds a level of believability to a movie if the actor's face can be seen clearly while a stunt is performed. This means that tricks used to hide stunt doubles (How many times have you seen an actor fall or roll down an embankment and they always end up with their arm covering their face?) can be forgone. Not to pick on one actor, but Tom Cruise willing to do his own stunts is probably pretty important to his movies, because there probably aren't a lot of people out there doing stunts who have a similar build and height.