I get Bulb bills and also get bills from my old provider. I wrote in and was asked to send a bill as proof, and since then I have had no responses.
One of the possible reasons for this is that because Bulb charge in advance, where as most suppliers charge after use, the first Bulb payment comes before the final bill from your old supplier. This happened to me.
I would still check that you are now all square with your old supplier and then cancel any Direct Debits you have with them.
@nicholas Have you since received Ursula’s response? It looks like you sorted this out, but please let us know if this isn’t the case.