Breakdowns reported within the bus system need to be addressed, he said.
"If they're doing proper maintenance, why in the world are these buses breaking down at this rate?" he said.
Espiritu also questioned why the city hadn't made handicap accessibility improvements sooner.
"Why, all of a sudden, is the city of Glendale concerned with ADA regulations?" he asked. "They had five years to start correcting this problem."
In 2005, city mechanics' inspections revealed several violations of the Americans with Disabilities Act on a number of Glendale Beeline buses, including leaking wheelchair lifts and broken grab rails, according to city reports.
The contract discussed on Tuesday should have been extended for a shorter amount of time, Espiritu said.
"They should extend this for a period of six months and start looking for a new contractor to provide the services," he said.
Council critic Barry Allen also addressed the issue, expressing some of the same concerns raised by Espiritu.
"If you're having all these breakdowns, if you're having ADA-compliance issues, maybe it's time to put [the Beeline] out to bid," he told the council. "Let's bring in another contractor or several other contractors. Let's put out a proposal and not make this a 15-month deal."
Representatives from MV Transportation could not be reached for comment.
"I'm not particularly enamored with this company either," Councilman Frank Quintero said. "I'm not exactly sure there are any operators out in the world that are going to be any better, and, actually, the one prior to this company, I think, was a lot worse. So we've moved up."