The Brazil international's name dominated the headlines after Wednesday's contentious Copa del Rey clash with Atletico Madrid at the Vicente Calderon.
The forward not only decided the game - and the tie - in his side's favour with a classy double, but also suffered much of the home side's frustration.
Neymar was reportedly confronted by Atletico boss Diego Simeone and midfielder Gabi during the half-time interval - an incident which allegedly prompted the dismissal of the latter.
Atletico have subsequently denied that any such clash took place, but Gabi did label Neymar's behaviour during the game "irritating", while the former Santos man subsequently demanded that he be afforded more "respect".
Bartomeu has now saluted Neymar for the way in which the 22-year-old is standing up to the extra attention and scrutiny to which he is now being subjected.
"We currently have the best player in the world, which is [Lionel] Messi, and the footballing magic of Neymar, who is showing great maturity in his game without falling into the traps set by others," the Barca supremo told reporters.
"I am very proud of Neymar and how he is a person. We Barca fans really like his game and he is giving us a lot."
Meanwhile, Barca defender Jeremy Mathieu recently claimed that Messi and Luis Enrique had been involved in a training-ground argument during the winter break.
However, Bartomeu refused to be drawn on the apparent confirmation of tension between the Blaugrana's star player and his coach.
"I do not want to get into any controversy," he added. "The team are doing well and portraying an image that appeals to fans of the club.
"We have much to improve but we are in the middle of an exciting and successful season."
Barca currently sit second in La Liga, are in the semi-finals of the Copa del Rey and also through to the last 16 of the Champions League.
