I think the no-see-um wee midgey is a west coast problem ( maybe because east coast is drier and gets colder ? ), so you could go to east coast anytime.
We have been to Scotland many times, by car though, not bike, love it, roads seem perfect for biking - but seem to have rougher surface texture than
England, maybe because they get snow and ice more often 'north of the border'. Always been before may or during September when the midges are
not active, but you still have to look out for ticks - mainly in Aug / Sept but if you are not walking in countryside you are pretty safe as they don't
come looking for you like midges do..
https://outaboutscotland.com/midges-in-scotland/
https://life.spectator.co.uk/article...s-of-scotland/