From my experience (with my Monzo account where I get instant notifications of payments), it usually takes 2-3 days from the moment the direct debit ‘hits’ my account until it shows up in Bulb. My understanding (which is probably wrong) of the Direct Debit ‘cycle’ is:
Day 1) Merchant creates list of payments. Sends to BACS for processing as an ‘overnight batch job’
Day 2) BACs sends payment list to individual banks as an ‘overnight batch job’
Day 3) Individual banks debit the person’s account. Individual banks report back to BACs which have been successful/failed - again as an ‘overnight batch job’
Day 4) BACs collates all the responses it has and prepares to send them back to the merchant as another overnight job.
Day 5) The merchant finally finds out who has paid.
BACs is ‘closed’ on weekends and bank holidays so that can add delays to the times. Direct Debits is a ‘reasonable old’ technology designed to work with ‘old fashioned’ banks which gave customers statements once a month - so it doesn’t quite ‘cope’ with today’s instant notifications/up to date statements.
[Remember, this is just my personal understanding and it might not be ‘BACs’ who are responsible for Direct debits and the timeline may be slightly off, but that’s how I tend to think of it]