Yes, certain bus services were routed through George Street before the tram. The 10, 11, 12, 16, 42, and 100 airport service all appear to still travel along George Street. There are quite a few buses that cross George Street at Frederick and Hanover Street but don't travel along the street itself.
Whether that justifies SIX bus shelters is another matter. If you look at Lothian Buses route map, only one short section of George Street still carries buses: between Frederick Street and Hanover Street in both directions, and eastward from Hanover Street to St Andrew Square. So any bus shelters outwith those sections would be unnecessary, except of course to carry advertising for JCDecaux's clients.
Maybe a wee map showing all the locations along George Street will be required to get a feel for how many shelters will be "surplus to requirements" from a transport standpoint?