Bartra, a product of Barca's youth system, only became something of a regular feature last season as he made 17 La Liga starts.
The 23-year-old also agreed a new three-year contract with the club earlier this year and looks set to take advantage of a lack of central defensive options during Luis Enrique's debut season in charge.
With long-serving skipper Carles Puyol having retired, Bartra is eager to stake a claim for a place in the heart of the defence as Barca seek to regain the Liga title from Atletico Madrid.
"I want to establish myself and get plenty of playing time, so I can contribute fully to the team with all my ability. This is my third season and I feel confident that I am ready to take a step forward," he said on Tuesday.
"[Luis Enrique's] message is that we all have a part together and that we need to pull in the same direction - we have to win our place in the team in every training session.
"I am hoping to convince him that I should be in the starting line-up from the first game of the season, I spent my first two year as a professional and I have great memories - I learnt that winning mentality from him- that's what he taught us all."
Barca have been heavily linked with a move for Valencia defender Jeremy Mathieu as they seek to help plug the gap left by Puyol's departure.
However, Bartra is confident he has the experience needed to step up, having featured in the Champions League over the past two seasons as well as scoring in the Copa del Rey final last term.
"It's my third year and I've been through a lot, from not getting a sniff to playing a bit and then getting picked for big games," he added.
"Now I feel mature and excited about giving all I can to the first team. There will be more competition and we will have to grit our teeth and fight for a place in the team."