For some reason, I feel the need for some indication of the space being traversed. I find support for that here:
barrel VERB INTRANSITIVE INFORMAL UK 1 to move very quickly in a deliberate or determined way
barrel down/into/through etc: David was barrelling down the hall towards her.
Thus, I personally would be more comfortable with, e.g.
the boy in the wheelchair was barrelling down the path toward the laughing bullies
I notice that the verb is described as British. If so, then the spelling requires double "l" - "barrelling".
If however the usage is known in the US, (and your story takes place there) a single "l" is correct.