Are you sure that there is an "s" at the end of "character"?
if X is bursting with Y, X has a very, very large amount of Y (like a suitcase that is bursting because you've filled it with too many clothes.)
"This is an excellent dessert. It is absolutely bursting with flavor.""
character (uncountable)= what makes something special, unique, and good.
If a street is bursting with character, it is very different from any other street in the world.
a character (countable)= a person who is interesting but slightly strange, like a juggler
If a street is bursting with characterS, it contains a lot of jugglers and actors and artists and magicians.