The simple answer is 'it depends'
To start with, scheduling buses is not as exact a science as timetabling trains. Even at 'timing point' stops, the traffic commissioners 'timekeeping window' is that buses should be no more than 1 minute early and no more than 5 minutes late departing, 95% of the time. There are a lot of unknowns including other road traffic (one badly parked delivery van, or following the dustcart, can make a big difference to odd journeys on odd occasions, for example) and each passenger transaction is an unknown (more so outside London) and there will be the occasional stop where there's passengers with mobility issues, or push-chairs, who need a bit more time to get on and off safely.
In London, most of it is in TFL's hands - they specify times of first and last bus, and frequencies during different parts of the day / week. TFL have bus stop design standards which vary depending on how many buses per hour are expected to use it. On paper, it's in TFL's tender specifications that operators should try to space buses on route X to run at an even headway with route Y that shares the route between these points and with route Z that shares the route between those points. Although in practice, it's not always possible to do that within the tender specification that TFL put out (frequencies may be different at least some of the time), and doing it is likely to cost additional service journeys both to do that and comply with the basic specification, so operators tend not to give much if any thought to it, and TFL don't seem to when assessing tenders. Operators are not going to want to offer a bid that complies with that if it will cost more than a bid from an operator that doesn't bother.
TFL tend to specify maximum number of buses on any route can be scheduled to be on each stand at any one time. TFL also have right of veto over where operators can do on-route driver change-overs if it's got the potential to cause problems for other buses / traffic.
(London Bus Route Histories site includes current or last set of tender specifications for many routes - example on route 1 page
here, button towards the bottom of the page.)
Outside London, there are a few examples where local authorities, in consultation with the traffic commissioners have imposed a limit on the number of buses / buses per hour on particular roads - the only ones I'm aware of (which of course doesn't prove the absence of others) are Sheffield City Centre in the early 90s when the city was more or less gridlocked with buses, and (from memory) a limit on sightseeing buses in (I think) Bath. This is a power in the 1985 Transport Act (as amended) but is rare enough to be newsworthy when it's invoked.
But unless it has been invoked, there's no restriction on competing operators using the same stops / roads and competing with each other.
Operators will generally liaise with bus station owners over allocations of routes to particular stands, and this can be a can of worms where there are competing services, and more so if one operator owns the bus station.
There's no compulsion on operators to co-ordinate their own services, although many will try and have an even headway between A and B when there's one route that runs A - B - C and another route that runs A - B - D. Although this isn't always as simple as it looks if the time taken to go from B to C and back isn't the same as (or a multiple of) the time it takes to go from B to D and back, or if the routes don't warrant the same headway. And there may be times when there's a sound traffic reason (particularly round school or college or works journeys) for multiple buses to arrive and depart at the same point close to each other, or for odd journeys to step outside the regular headway.
It depends what a scheduler's been told to do on any particular occasion - it may just be that a new timetable is needed urgently for route X, there might (in theory) be time for a full network review (although the latter will also include more variation fees, and costs of producing more printed / electronic information, as well as schedulers' time.)
But many planning / scheduling teams are under-resourced - smaller operators often don't have specialists, and the manager is expected to do it all, many 'big group' operators have teams centralised at regional offices - who can end up trying to do several changes across multiple local operating companies at the same time, and the people doing it may not have the local knowledge that's an important part of doing it well.
Route timings is another one where there isn't a simple answer. Some operators have gone down the marketing friendly approach of having buses at exactly the same time past each hour at all points all day, so a bus at 0600 Saturday has the same running time as one at 1700 on a weekday. Which means some buses will run late, and others will be standing to wait time at every timing point, which annoys drivers, passengers and residents of homes near the timing point. (and passengers waiting at intermediate points, where a bus will often 'run early' compared to the calculated 'approximate time' that Traveline / Bus Times etc works out based on an even speed between stops.)
Some other operators have gone down the path of analysing data so much that every journey through the day is subtly different, even if it's the odd minute or two here and there.