Do you need something like Fitnesse, if you have BDD tests?
While BDD is larger than the scope of just tests, there are indeed BDD tests. These tests are Unit Tests that follow the BDD language.
Given some initial context (the givens), When an event occurs, then ensure some outcomes.
There are a few good BDD frameworks available depending on your language of preference. JBehave for Java RSpec for Ruby NBehave for .NET