Bruce made 11 signings during the summer transfer window in an effort to bolster his squad, but has since seen striker Asamoah Gyan make a shock loan move to United Arab Emirates side Al-Ain, while on the pitch the Black Cats have started the campaign without a win in five games.
That run has included a derby defeat at home to Newcastle, as well as a Carling Cup second-round exit at the hands of Brighton.
The Wearside outfit head into the Barclays Premier League clash with Stoke at the Stadium of Light with the pressure on Bruce, but Potters boss Pulis is confident his counterpart will not let Sunderland get stuck in a rut and that he and the club "will be fine".
Pulis said: "Steve Bruce is a great manager, he is at a great club and you have difficult times - that is management, it is a really difficult job.
"The aspirations of people connected with clubs now is far beyond what most people can achieve but that is the way we live our lives.
"Expectations and aspirations of fans at every club up and down the country far exceed what is reality in lots of respects, but you have to deal with it and manage it.
"Ninety per cent is managing expectations but you have to do it if you want to be in it.
"Steve and the club will be fine. He is a strong and competent person who will enjoy the challenge.
"You need a bit of time to bed in new players. He's been unlucky with John O'Shea's injury and the situation with Asamoah Gyan, but that happens.
"He won't want me trying to tell him what to do.
"Football is like life, it goes up and down. You have to take the good times and bad times and deal with them in the same way."
In contrast to Sunderland's troubles, Stoke have made an impressive start to the season.
Having got things under way early due to their participation in the Europa League qualifying rounds, the Potters are unbeaten in nine matches and have taken eight points from their first four league fixtures.
Pulis is never one to get carried away, though, and insists that for now, his primary target remains keeping the Staffordshire club in the top flight.
"We have to keep our feet on the ground," Pulis said.
"We ask and demand the same commitment and energy levels that the players have shown.
"We need to get 32 more points because safety is our first aim - and that will never change at this club.
"We don't feel as though we are in front of the game. We are working as hard as we can to stay in the Premier League."
Pulis will check on the condition of a host of players ahead of Sunday's contest.
Several squad members did not travel to Ukraine for this week's Europa League Group E opener against Dynamo Kiev, with record signing Peter Crouch - a target for Sunderland before he joined Stoke last month - staying at home as a precaution after missing training, and Matthew Etherington (back), Rory Delap (groin) and Marc Wilson (hamstring) also absent from the trip.
That quartet and Jonathan Woodgate, who is not registered for the Potters' European campaign and has been working to shake off a minor injury, are among those that will be assessed, while goalkeeper Asmir Begovic - rested for the Dynamo game - is expected to return to the first XI in place of former Black Cats stopper Thomas Sorensen.