I agree with the timer suppestion. My daughter did this too, and so I made sure we had nothing going on for a few days and we stayed home so we could focus on the potty. I started out with 10 minutes, and then go from there to increase the time. Her reward was if she went potty she got to help me reset the timer (the minute timer on the microwave), if she didn't no reaction either way. My girls called it the "potty beep" and knew when they heard it to stop everything head to the potty. They still head in when dinner gets done and the timer goes off :), so it obviously worked.
For accidents I leared a technique from a book called "Early Start Potty-Training", and it only suggests this once your child has "Uh-oh it looks like Suzy had an accident. You don't go potty here, you go in the bathroom. It looks like you need somemore practice." Then you walk them to the potty pull down their pants and sit them on the potty, telling them, "This is where you go potty". Then you pull their pants back up (yes they are wet) go back to the spot where the accident happened and repeat th process for a total of 3x. You say all of this very matter of fact, without any emotion. I know it soulds weird, but with both of my girls I only had to do it twice and that was it.
Also, for on the go with girls the best thing ever is the "Potette" it is a portable potty that you can use on the go, and it folds flat. I got it at Burlington Coat Factory. My girls prefer that to going to public restrooms.
Good luck!