Chain is right on the money with his advice! But there are some things that precede your action.
1. Call the police since even though they were not there when you went out. You can bet they were probably still in the area seeing what they could steal.
But to start, if the area of your bike is in view from a window or around a building it would be best to observe the area for a while first. This might keep you even armed, from walking into a bad situation or worse. They could be armed and ready or have a lookout or backup individual. An example from experience, a guy was having his car broken into in a apartment complex in the city. He went charging out of his apartment to the car and was shot and killed immediately right there on the sidewalk. Never had a chance to defend himself. So gets back to the point. if I were going to go out and approach anyone stealing my bike, you bet I would have one cambered and the gun out of the holster or wherever it is carried.
As Chain stated in most states you can not use deadly force in theft cases unless you are threatened with serious bodily injury or death yourself. Obvioulsy if they pulled a weapon and aimed it at you or shot at you that would constitute the use of deadly force but only then.
But I believe it is a great idea that anyone who carries or has a weapon for self defense should get some profesional training, know how to operate the weapon, become proficient and know the Law. The NRA has some good classes as do some shooting facilities. But get some references on outside trainers. There are a lot of so called instructors out there only sucking up bucks with little training experience. "Wanabees!
Good luck and I am glad this particular incident came out in your favor!