The bus veered off Lake Shore Drive Saturday evening and into a group of trees.
The CTA is conducting an investigation into the cause. But the bus drivers' union said Monday it should be done by a third party to insure the integrity of the findings.
The union also raised questions about the safety of the CTA fleet, saying outside vendors perform some repairs.
A CTA spokesperson released a statement saying, "we have a skilled investigative staff that knows how to conduct a thorough, fair and fact based investigation."