It depends. If the speaker wants to have a way to get back, then the meaning is negative.If he/she needs a change and is not willing to return, then the phrase has a positive meaning.

As Lliyana mentioned, it depends mainly on the situation. To burn one's bridges means to act or behave in a way that makes a certain action or situation impossible to change or stop. It is usually an unpleasant or dangerous situation,so it will many times have a negative connotation. For example if one was hoping for a promotion and upon a debate with his manager walks out angry from his office ,the person might burn their bridges. Due to his/her conduct the chance of getting a promotion is irrevocably impossible.In this situation it is negative. However if staying in that job wasn't that rewarding, then not getting a promotion or having to quit the job altogether might be an opportunity to look for a better well paid post. Here burning one's bridges by loosing the job for example could be regarded as a positive thing.