"I was very proud of the way we came back and won the third and fourth games," said Coach Lynn Larson.
But the Sissies opened the fifth game with several unforced errors and couldn't recover, dropping the game and the match 15-5.
Bowie won the opening game 25-18 and took control with a 25-17 win.
But Bridgeport won two tight games 25-22, 27-25 to force the match to a fifth game.
"I still feel like we are improving and will keep working hard in practice to get ready for district," Larson said.
District play begins at Wichita Falls Hirschi Friday, Sept. 25.
Jordyn Hulsey set up 49 assists in Tuesday's match, with Haley Meekins turning 16 into kills, Jessica Hartsell had 11, Alicia Erwin nine and Becky Grinnell six. Meekins blocked two attempts and Erwin one.
Lindsay Zachary led the service game with five aces of the team's 15, Katie Cook had four and Lauren Richey three. Richey assisted the defensive effort with 15 digs, Meekins added 14, Hartsell 10, Cook and Zachary five each and Hulsey three.