Bale’s booking came not long before Wales defender Neil Taylor was sent off for the challenge which left Seamus Coleman with a broken leg.
Bale must serve a one-match suspension after picking up his second yellow card of the World Cup qualification campaign.
Chris Coleman’s 10-man side survived a late Irish onslaught to claim a point in Dublin.
Davies joins Gareth Bale, skipper Ashley Williams, Joe Allen and Joe Ledley in being one booking away from missing the trip to Serbia in June.
The battle for places at next year’s tournament in Russia has reached the halfway point.
Bale was booked and O’Shea was able to play on, but later had several stitches put into a wound on his shin.
Taylor spent eight months out of the game after breaking his ankle in 2012.
The striker comforted his team-mate on the pitch and is confident that he will return to his best after the lay-off.
The car manufacturer has been the leading partner of the Home Nations since 2011.