Most bus services in the UK are governed by UK Domestic driving hours rules. Only those that go over 50km in length fall under tacho regulations for which there will be a separate thread. This information is taken from the GOV.UK Drivers hours page and provided here for your reference.
Breaks and Continuous Driving
After 5.5 hours of driving you must take a break of at least 30 minutes when you must be able to rest and take refreshment.
Or, within any period of 8.5 hours, you must take at least 45 minutes in breaks. You must have a break of at least 30 minutes at the end of this period, unless it’s the end of the working day.
You must not work more than 16 hours in any one day - including non driving work and any times when you’re off duty.
Daily Rest Periods
You must take a rest of 10 hours between 2 working days. This can be reduced to 8.5 hours up to 3 times a week.
Fortnightly Rest Periods
Every 2 weeks you must take at least one period of 24 hours off duty.
The GB Domestic rules don’t apply if:
1/. You don’t drive on the public road, eg if you drive as part of work in road maintenance, quarrying, construction work, civil engineering works 2/. You drive for less than 4 hours in any day
For the purposes of UK domestic driving hours, a fixed week is from 00:00 on Monday to 23:59 on Sunday.