Speaking on Saturday’s BBC Sportsound programme, Budge raised her concerns at four sets of supporters convening in Glasgow on the same day for two high-profile matches.
She said: “Clearly, no one believes this is a good solution. I don’t believe the SPFL thinks it’s a good solution.
“For whatever reason, they feel their hands are tied and they can’t come up with an alternative.”
“Fans will be arriving early to go for a pint, they will be going to the pubs after the first game. It really is a big problem,
“I guess from the SPFL’s perspective, all they can do is ask Police Scotland ‘are you happy you can handle this?’ and, apparently they have said yes.”
Budge was also critical of the kick-off times for both fixtures, calling them “totally unacceptable” and something that “flies in the face” of attempts to encourage more fans to Scottish football.
She continued: “We’ve been back and forth with suggestions but, in terms of the fixtures, everything we came up with was met with ‘that can’t be done because...’
“I know how hugely complex this all is but I think we almost have to forget some of the constraints and think out of the box. I will continue to press for an alternative. I will keep pushing.”
The SPFL’s Chief Executive, Neil Doncaster, responded to criticism on Friday, acknowledging the inconvenience to supporters but citing a congested fixture list and contractual requirements to play at Hampden for the decision.