Bowe was dropped for the opening Pool D victory over Canada but responded by scoring two well-taken tries against Romania at Wembley on Sunday.
He was "happy enough" with his performance in his 64th test -- bringing up 150 points in international rugby -- but knows a place in the starting side to face Italy on Sunday is no certainty.
“It was great to get back out and see the ball being moved about. To score a try or two was nice,” he told reporters on Monday.
"The competition for the back three places is something else. Myself, Keith Earls played exceptionally well, Simon Zebo played well and Rob Kearney looked full of energy when he came on.
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"All I can do it put my hand up when I am given the opportunity.”
Bowe, 31, paid the price for a below-par performance in Ireland's 21-13 warm-up defeat by England with the winger at fault for Jonny May's try.
“I was disappointed. I would normally be relatively consistent with my performances, but that day was definitely one of the more difficult ones," he said.
"But I bounced back and put it behind me relatively early. I was excited to get back on the pitch again after you put in a performance not the way you want to play.”
It was fitting that Bowe should serve a reminder of his clinical finishing against Romania having been the lone survivor in the Ireland side from when the teams last met in 2005.
Bowe surged over and touched down in the right-hand corner after a sweeping first-half move and got his second score just after the hour when Ireland attacked from the back of the scrum.
Left wing Earls also touched down twice and Zebo was a constant menace with his willingness to attack from deep in an all-round impressive Irish backline display.
“Simon is pushing Rob (Kearney) hard for his place at fullback. He is a very exciting player and he has showed that he is capable of doing the basics right. It shows that we have more than enough people to come in and do a good job for the team,” Bowe said.
"Every player wants to give the coaches a headache. We all feel we are good enough to be playing week in, week out."
(Editing by Ed Osmond)
