Bauer is the first Chicago police officer killed since 2011 and is "the highest-ranking officer killed in decades".
Officers also returned to the Thompson Center on Wednesday morning, showing commuters a photo of the suspect.
Shomari Legghette has been charged with first-degree murder in the shooting that occurred Tuesday in the city's downtown.
Both the wake and funeral for Bauer will be held at Nativity of Our Lord Catholic Church in Chicago.
Guglielmi said that Bauer had been attending training at the Chicago Fire Department with other officials before the shooting.
She told the paper that she saw officers lead the shackled suspect away and put him in a squad auto, and then watched as emergency workers administered CPR to Bauer, who was lying on a stretcher, before he was put inside an ambulance and rushed to the hospital.
Some footage was captured by a cab driver who saw Bauer chasing Legghette on foot across the street into the Thompson Center.
Mayor Rahm Emanuel called Bauer's death "a tragic reminder of the unsafe duty the men and women of our police department accept to ensure the safety of us all". It was at that point the suspect shot Bauer in the head, police said.
Bauer, a veteran of the Chicago Police Department, was fatally wounded when he approached an armed suspect whose description had come over the police radio. The person spoke on condition of anonymity.
A suspect is in custody.
Department spokesman Frank Giancamilli wouldn't comment on the weapon but says the suspect was also wearing a bulletproof vest under a coat.
A convicted felon has been charged with first-degree murder in the shooting death of Chicago police Cmdr.
The 53-year-old Bauer, wearing his police uniform, was in his auto after having lunch near the James R. Thompson Center, a downtown government building, when he heard the call, police said Wednesday.
Bauer, 53, is survived by a wife and daughter, Chicago Police Superintendent Eddie Johnson told reporters Tuesday, as he teared up.
Bauer was rushed to Northwestern Memorial Hospital, where he was pronounced dead a short time later.
(Above) 18th District Police Commander Paul Bauer speaks at the annual meeting of River North Residents Association on November 14, 2017.
Police spokesman Anthony Guglielmi (goo-lee-EHL'-mee) said on Twitter late Tuesday that Bauer was on-duty, not off-duty as previously reported.
Johnson said officers initially confronted the suspect because he was acting suspiciously. He didn't provide further details.
"I ask each of us, in the days ahead, if you see Chicago's officers doing their job, reach out to them as a member of your family". We're talking about career robbers, burglars, drug dealers. "They need to be off the street".