So what would happen to drivers in these circumstances?
Hard to say as we don’t know the exact details of the situation, it may not even be the drivers fault at all & down to the controller - I know of one instance where a controller mistakenly announced a diversion & although he corrected himself 30 secs later, a bus had already gone the wrong way (admittedly this is rare though).
The most likely situation is that it’s a brand new driver or a driver new to the route in which case the worst they’ll get is a rollicking from the duty manager - one wrong turn is not going to get them a disciplinary or sacked as long as they safely corrected their mistake which it sounds like the driver did in this case. Also drivers are not given adequate time to route learn during training (drivers are basically expected to learn in their own time) so this will be taken into consideration as well. It also costs thousands to train drivers for a D licence so bus companies aren’t going to sack you for minor reasons.
I’ve known rookie drivers who have gone the wrong way & ended up in worse situations then the one in the OP, there have been buses stuck in fields & had to be towed out, buses going the wrong way down a one way street & causing traffic jams & even one who mistakenly went down a narrow lane in a double decker & ended up stuck as he couldn’t reverse due to the traffic behind nor could he go any further due to a low bridge (the traffic police had to be called to help clear that one!) & they all kept their jobs.
In the grand scheme of things one wrong turn for a new driver isn’t that big of a deal especially as it didn’t cause an “incident” i.e no damage to the bus, no outside agencies needed to be called etc. From the OP it sounds like the driver spotted his mistake almost straight away & took corrective action instantly to get back on his route, the fact that there was traffic on the detour which caused a delay is unfortunate but it’s not like the driver was driving around aimlessly lost for 40 minutes which would be more serious.
If on the other hand, it was an experienced driver on his usual route & he/she couldn’t provide a satisfactory reason for the wrong turn then they could be looking at a warning, extra training or possibly dismissal (if they already have a number of warnings or if there was gross misconduct etc.)
I will say this though, there are official disciplinary rules & procedures from the bus company head office (possibly what the OP’s BIL from TFL is referring to) but bus garages usually apply them very loosely for minor infractions - the duty manager will usually decide to give you a telling off & slap on the wrist rather than writing you up, again only for minor infractions though.
Correction I mentioned ibus in a previous post, ibus is only in London, bus garages outside of London use different AVL (Automatic Vehicle Location) systems!