Glasgow City Centre is a pretty safe place. At that time of the morning the street sweepers will be out, and the last of the very tired drunks from the night before. They will be so tired as to be no threat. At this time of year it is already daylight by 5am.
The 0545 arrives at Edinburgh Airport at 0641. I think I might pitch for the 0515 arrive 0611. Just belt and braces in case of any traffic delays.
Several people have commented on other social media in the last week or two that Citylink are encountering staffing issues at the moment, with a level of cancellations happening on high frequency services. This isn't just idle talk- I am aware of a documented case of an Inverness to Glasgow cancellation, which was filmed by a you tube creator, by chance. So travelling one bus early gives a comfort level.
It's hard to know what it will be like at the Airport so early. The advice is always 3 hours for an international flight. Bear in mind there are a lot of early flights on the budget airlines- so the airport may be busier than you expect.