There are 3 main companies up here and there isn't much cohesion between them! There are a few multi-operator tickets but the longest you can get them for is a month - the Student "Network One" (purchased on GoNorthEast app) would likely be the one you'd go for if you're a regular bus and metro user. Stagecoach I believe do an annual pass but it would only work on their services and not GoNorthEast or Arriva.
Single tickets atm are £1 if you're 21 or under and £2 if you're 22 or over so unless you get the bus regularly that's probably the best bet. Ultimately unless you're going/living a decent way outside of the centre I can't see you using the buses much at all.