The Football Association said the 30-year-old was charged after the goalmouth altercation was missed by match officials but caught on camera.
Forward Freda Ayisi, making her league debut for Birmingham, was sent off in the 45th minute.
Video footage posted on the internet showed Ayisi elbowing Bardsley in the chest, with the U.S.-born goalkeeper hitting back before more blows were thrown.
Bardsley subsequently apologised on social media for what had happened.
“Passions ran high against Birmingham yesterday. Viewing the footage again, I regret the incident with Freda Ayisi,” she said on Twitter on Monday.
“Whilst I was provoked, it was out of character for me to react in that way. I’ve contacted Birmingham to apologise for my involvement.”
(Reporting by Alan Baldwin, editing by Justin Palmer)