You could just telephone Stagecoach to ask
All we can do on here is speculate which isn’t going to help.
Or you could use that Google thing and you’d find that it is all covered on their website here: https://www.stagecoachbus.com/conditions-of-carriage in section #9
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One accompanied, well-behaved dog or other small animal which will not be a danger or a nuisance for other customers or our staff is allowed to travel with you on our buses at the discretion of the driver who may reasonably decide where on the bus the animal is best carried.
A fare may be charged for dogs and details are contained in the ‘Guide to Tickets’ of the local Stagecoach operating company available on our website.
Where appropriate, dogs must be muzzled or put on a lead in accordance with the Dangerous Dogs Act. Small animals must be caged, boxed or kept on a lead. Any animal carried must remain under control and must not be allowed to sit on the seats.
If you bring an animal onto a bus, you will be held responsible for any damage, loss or injury arising from its presence on the bus.
Guide dogs, hearing or assistance dogs accompanying registered disabled persons are carried free of charge at any time. Assistance dogs should wear their harness or identification jacket when travelling.