Peak time is late-May through to mid-July (presumably the riders unaffected by school holidays) and then another blip late-July to mid-August.
The daylight hours in June are very long in Scotland (we were at JOG on 20 June and there was barely any darkness) which allows longer riding times .. and, of course, weather may be better (but don't bank on it!)
The other factor cited for an early season ride is the risk of midges in Scotland - although they seem to have been upset and confused by climate changes and rainfall patterns in the last few years.
Summary : Other than periods of obvious extreme weather, any time is pretty much OK
TIP: For midges, use the Avon Skin So Soft product ... they just hate it [All the ghillies in the Highlands have a bottle in their Barbour jackets]