They now face fines totalling more than £600,000, if they fail to pay up in 14 days.
Last month, John Taylor was caught going through the bus gate at Nelson Mandela Place.
He insists he did not see the warning signs, which he has since described as "woefully inadequate".
Mr Taylor, an architect, lodged a freedom of information request with the city council asking how many cars contravened the bus gate from the day it went into operation on Monday June 30 until Wednesday July 16.
On one of the days the camera was not in operation but, on the remaining 15 days, it caught a total of 10,096 motorists.
The lowest number of breaches was on the first day of the new scheme, when 477 were nabbed, and the highest on Friday, July 4, when 802 went through the bus gate.
Each motorist will be hit with a £60 fine, reduced to £30 if paid within 14 days.
Mr Taylor said: "I have no problems with bus lanes and improving traffic flows but the problem here is the bus gate is so badly signposted."
He insisted the signs are often blocked by buses, leaving motorists with no way of knowing they are about to break the rules.
Mr Taylor said: "The sign in West George Street can often by obscured by traffic or a parked van.
"If they really wanted to curb private cars going into George Square they would signpost it fully."
He insists he will not pay the fine and plans to appeal.
Neil Greig, of the Institute of Advanced Motorists, said the city council had failed to get information about the bus gate over to drivers.
He added: "Clearly there is a complete failure of signpost information when so many people are getting caught"
A city council spokesman insisted the new traffic restriction is well signposted.
He said: "The majority of drivers don't receive fines as they don't choose to drive through a well publicised and very visible bus gate.
"The number of offences has dropped by 65.7% since the bus lane enforcement began and we expect further reductions.
"Seven permanent signs advising the bus gate is operational have been in place since the beginning of June and are clearly visible on Hope Street, West George Street, West Nile Street and at Nelson Mandela Place.
"In addition, there were two temporary signs on Bothwell Street and West George Street in the run up to the bus gate coming into play."