We have used the buses many times, there are special TT timetables, extra buses & 'night owl' (late night buses).
We've used them at all times of the night & day, sometimes it's been packed, sometimes not. 
The TT timetable should be available online.
Word of warning - depends where on the course you are, but the first bus after roads open will probably be full, & the 2nd one!
by then the empty buses will overtake the ones stopping & it will improve. Also, of course, the bus may set off from Ramsey (or Douglas, or Peel) at roads open & then have to get where you are! No problem if you're at a pub/cafe, then you can have a drink while you wait!
Buses don't tend to arrive early after the first couple of stops. 
There is (was) a great bus tracking app, that really gives you an idea of how long the wait will be for the next bus.


One Mad Sunday night, after the forum meeting at The Old Market, myself & Mr. Led went for the last bus, after midnight I think it was, to the bus station.
We saw a bus leaving, but waited a few minutes & a few more, then a Bus Vannin transit van went past us & turned round & stopped by us. He asked where we were going & we told him Peel but the bus hadn't turned up. He said that it looked like the bus had left a few minutes early, but he would radio thru' & get him to come back. Then he drove off. After a few minutes we were beginning to think we'd been 'pranked' & decide we'd have to get a taxi. Lo & behold, just then a bus came down the road, turned round at the roundabout & stopped next to us. He asked if we were the ones going to Peel & said that he'd been 'requested' to come back for us. He apologised profusely, explaining it was ultra quiet that night (wouldn't have been like that 30 years ago!) & he'd set off early. It was true that we were the only ones the bus & we did had a laugh on the way back! Never have I travelled on a double decker bus so fast!! i think we must have been getting on for 70mph in places, never stopping & getting to Peel about the scheduled time!
(Parts of this story may not have occurred exactly as billed, we'd been in The Old Market all night & Daves hospitality was legendary!!😂)