Graham's drought is becoming a frustrating sub-plot for Bruce on what has been an otherwise impressive return to the Premier League for the Tigers.
The on-loan Sunderland forward has made 13 appearances without finding the net this season, but his lean patch goes back much further than that numbering 30 games for three different clubs since he struck for Swansea in a 2-0 league cup win over Chelsea.
The 28-year-old has impressed at times with his leading of the line and hold up play, but has lost composure on a number of occasions after getting into promising positions.
Hull visit the Liberty Stadium on Monday evening and Bruce hopes his former employers can bring out the best in Graham.
"I keep getting the same thing thrown at me about Danny and he's got to see it through like any other striker," he said.
"Could Swansea be the one that turns him around? We have to wait and see, but you never know.
"We saw something like that the other night when we played Arsenal. Nicklas Bendtner hadn't scored for them for two years, we'd tried a little bit to get him in the summer, I've signed him twice in the past...did Arsene Wenger do it on purpose?
"If he did he's a better genius than I thought he was.
"But all strikers go through it. No matter how good you are, there comes a time in your career when go you go through a lean pitch.
"One thing you've got to do is knuckle down and try not to lose confidence."
Hull skipper Curtis Davies, who will return to the side at Swansea having been suspended for the 2-0 defeat at the Emirates, is fully supportive of Graham.
He admits his team-mates have not spared the striker a few good-natured barbs in the dressing room, but Davies believes everyone appreciates his all-round contribution.
"We still give Danny a bit a of stick, a bit of banter, and I think he'd feel uncomfortable if we weren't doing that," he said.
"At the same time when we need to gee him up we do.
"The work he does for us as a team is great, he just needs one to deflect off him and go in the back of the net.
"Maybe the goals aren't coming because he's working too hard for us and he finds himself in positions where he's retreated to help the midfield, not in positions in the box where he can nick the tap-in.
"That's credit to him because he's rolled his sleeves up but I'm sure he'd like a goal too.
"It would be brilliant for Danny to nick one at Swansea. He's well-liked there and had a very good time there."
If Graham's barren streak does persist, Bruce is close to giving Matty Fryatt his chance in the Premier League.
Fryatt managed only five appearances last season due to an Achilles injury and was sent on loan to Sheffield Wednesday early in the current campaign.
But he is back now and eager to push his claims.
"I've never really seen Matty play because he missed a year with his Achilles, but thankfully going to Sheffield has done him a bit of good and he's come back into the fold," Bruce said.