Bounded waiting and starvation free in critical section problem
No, starvation-free doesn't imply bounded waiting.

For instance, consider a procedure that never even attempts to acquire any lock; but the amount of time it takes is variable and can be arbitrarily long.  Then there is no bound on the amount of time it might take to complete its operation.

Here is another example of how it can fail.  Starvation-free means that every attempt to acquire the lock eventually succeeds -- but that says nothing about how long it might take.  Maybe the amount of time it will take to acquire the lock is variable and can be arbitrarily long -- there is no upper bound on how long it takes to acquire the lock.  Then a procedure that first attempts to acquire the lock before doing anything else won't satisfy bounded waiting.