The 22-year-old finally made his Owls bow in their Carabao Cup triumph at Rotherham United on Wednesday evening - nearly three weeks after joining the club on loan from Hamburg.
Bates was one nine changes as Wednesday secured a place in the third round of the competition and a plum home tie with Premier League Everton next month.
The fine early-season form of first-choice central defensive pairing Tom Lees and Julian Börner has left Bates having to play a supporting role in the Championship.
But the Scot hopes his assured performance alongside Jordan Thorniley at the ASSEAL New York Stadium has given caretaker Wednesday manager Lee Bullen food for thought ahead of their league clash with Queens Park Rangers this weekend.
Bates said: "He (Bullen) has told me that I need to bide my time.
"The boys have done well. That has been his message and I have been trying to train as hard and as well as I can.
"The boys have been doing great in the league, so you have to hold your hands up at times.
"There is a lot of competition here. We have got some top players, so I have had to wait for my chance and try and take it when I get it."
The former Rangers player, who is set to remain at Hillsborough until the end of the campaign, admits he is enjoying life in South Yorkshire.
"I know a couple of the boys from the Scotland squad so that has helped me settle in quick," he said.
"All the lads are great. They are good footballers and good guys off the pitch as well."
Bullen is likely to recall a number of his top performers for the Hoops tussle. Keiren Westwood, Lees, Börner, Sam Hutchinson, Barry Bannan, Kieran Lee and Steven Fletcher are all expected to return to the starting XI.