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1.
cut off all ties in a relationship
when you burn a bridge you can't cross it again. to burn a bridge means to be completely done with something.
your bridges were burned
and now it's your turn
to cry, cry me a river
by mimi December 16, 2004
 
2.
street slang, the act of spraying(bombing, hence the term) a bridge with a lot of tags/throw-ups.

see "100 Grand Canyon" by Cancer Bats
And all the kids are bridge burnin', throwin' up their names!
And all the heads are street learnin', steppin' up their game!

"yo man let's go burn a bridge"
by ranimal April 03, 2008
 
3.
Burn a bridge is a slang term for lets go smoke some weed.
Can also say burn one
Hey you want to go burn a bridge with me?
by Rasta-Clat November 13, 2004