Bus from Edinburgh airport to Glasgow

Just buy on the bus using contactless.

That way it doesn't matter what time your flight lands. They are double decker coaches and run every 30 minutes so there should be no lack of capacity, especially as the coach starts there.
They leave from Stop D which is straight outside the exit door from Arrivals.

Thank you so much! This is exactly the information I needed.

Where does the bus drop you in Glasgow? A specific location or just the bus station?

It terminates at the Buchanan Bus Station, which is very centrally located, in the City Centre. Although you can walk from there to Queen Street or Central Railway Stations there is a free connector bus (if you have a train ticket) #398, which runs frequently from Buchanan.

All bus services (including the Glasgow Airport Express), except city services leave from Buchanan. One of the stops on the HoHo bus is outside Buchanan.

Almost all city services will call at George Square, outside Queen Street.

The closest hotel is the Holiday Inn Express, which is across the street.