Sorry to hear that - Bulb should have taken the first month ‘up front’ payment at the end of the switching process and then the next payment around one month later (for month 2). [edited: I did originally put at the ‘start’ of the switching process]
I would drop them a line on firstname.lastname@example.org (or give them a call on Monday - https://help.bulb.co.uk/hc/en-us/articles/115001240291-How-can-I-get-in-touch-with-Bulb- ) to see what has happened. It’s possible their billing system had a snafu, the initial direct debit may have been delayed in the banking system causing an overlap, there was a delay in taking over one of your supplies (for example, the electricity switch started straight away, but the gas one was delayed by a week or two and therefore you had two ‘start dates’ and two ‘starting debits’ - but the total of which is the same as the initial direct debit should have been) or there has been another sort of issue.
Absolute worse case scenerio, you’ve got the direct debit guarantee to fall back on (see https://www.directdebit.co.uk/DirectDebitExplained/pages/directdebitguarantee.aspx ) and whilst you could ask your Bank to reverse the DD ‘today’ it’ll probably be a lot lot quicker just to ask Bulb - I’ve heard banks taking several weeks to reverse any direct debits and Bulb should be able to (if there has been a mistake) issue a refund within 3-4 days (of course, if there hasn’t been a mistake and it was just something like the initial DD being ‘split’ and your bank does reverse it, that’ll mean you’ll go into debt with Bulb).