Officers responding to reports of an officer down saw Bachmann wounded on the ground in the front yard, then got into what McCollum described as an extended shootout with Caffall, who eventually was shot.
Both Bachmann and the gunman were later pronounced dead at a hospital. Police spokeswoman Rhonda Seaton said Chris Northcliff was outside the home when he was shot, as was the wounded woman, whose name had not been released by Monday evening.
The woman was hospitalized in serious condition following surgery. One of the injured officers, Justin Oehlkee, was treated for a gunshot wound in a calf and was in stable condition, Seaton said. Two other officers, Brad Smith and Phil Dorsett, were treated for "shrapnel injuries" and released, Seaton said.
Police declined to speculate on a motive for the gunfire.
The shootings prompted Texas A&M to issue an emergency alert warning students and residents to stay away from the area. Most of the university's 50,000 students were not on the campus about 90 miles northwest of Houston because the fall semester does not start until Aug. 27, university spokeswoman Sherylon Carroll said.
Diana Harbourt, 27, who lives about a block from where the shootings happened, said she heard five loud popping sounds from a back room of her home and looked out her front door to see an officer park his vehicle on the street and crouch in front of another vehicle.
"We heard him exchanging some words with the person and then shots being fired," Harbourt said. "And then we heard more sirens, and more officers and fire trucks came and they were keeping their distance, kind of slowly moving in. More officers showed up and told us to stay inside."
Officers, meanwhile, were dealing with losing someone McCollum called a respected colleague.
"Brian Bachmann was very close to everyone in law enforcement," McCollum said. "He was a pillar in this community, and it's sad and tragic that we've lost him today."
Bachmann worked more than 19 years in law enforcement, according to the Texas Commission on Law Enforcement Officer Standards and Education.