Uruguay striker Suarez moved to Camp Nou from Liverpool last month in a deal believed to be worth €94 million (£75m).
However, as it stands the 27-year-old will be unable to play for or train with Barca until October after he received a four-month ban from football for biting Giorgio Chiellini during his country's World Cup clash with Italy in June.
That ban could yet be reduced if Suarez's appeal to the Court of Arbitration for Sport (CAS) - the hearing of which will take place on Friday - is successful.
Suarez has bitten three players in his career, and it had been rumoured Barca had inserted a clause into Suarez's agreement that would result in his contract being cancelled should he do it for a fourth time.
But Bartomeu has now denied those claims.
"No, there is no clause," Bartomeu told CNN.
"If the clause did exist we wouldn't say it, but it doesn't exist.
"We didn't rethink the decision (to sign him) and we told Luis after the bite. He knows he did wrong.
"He apologised. That's very important for us.
"That means he knows that he did not do things properly - and of course, coming to our city, coming to our club, there's going to be a way of managing Luis Suarez, because at Liverpool he was a perfect player."
Bartomeu also revealed that Suarez turned down "better offers" to join Barca, and is confident that the forward will flourish in La Liga.
"When we approached Suarez, it was before the World Cup," Bartomeu added.
"We told him that he had the right age. He had the experience. Playing at Liverpool give him incredible performance also. And it was the right time for him to come to our club, to Barcelona.
"We knew from a lot of years ago that Luis Suarez likes our club, likes our city. And we have the advantage. His agent is [former Barca coach] Pep Guardiola's brother.
"He's from Barca in his heart, also, so everything was perfect and created the perfect atmosphere that Luis Suarez accepted.
"And we know that he had better offers than our offer but he came to Barcelona."
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