The Spaniard did win votes in Unai Emery's infamous poll which saw the players pick the club's next captain.
With current captain Pierre-Emerick Aubameyang now 30, Bellerin thinks he can step into the role when called upon.
"Obviously it's not the same when you're 14 or 15 as it is now because the responsibility and what you represent is completely different, but it's always been something that I've enjoyed. I enjoy positions of responsibility and I enjoy being the first one on that wall.
"For me, I had been speaking to the coach for a few months and he was telling me that I could be one of the people that could represent the team. I was really happy with it because I'm someone who's been here for a long time and I know how the club runs.
"People may not see me as this massive guy who shouts on the pitch all the time or what people may have as a captain in their heads, but there are so many different ways of leading a team.
"Everyone in the team respects each other and we have so many leaders who don't need to wear the armband to have an impact on how others think.
"After going through so many different captains and characters from my time here so far, you always get the best things from all of them. The time I've been here has been really useful for that and whether I was captain or not, I've always been someone who's liked to help and talk from the team's perspective.
"I'm not afraid of those things so for me, it's something I'm very proud of. I'm very honoured to be part of this group and it's something this team needs.
"I'm very happy that I was approached and then for the votes I received in the dressing room. That shows my team-mates trust me to do that job, and I'm happy to do it when I have to.
"In the group we have, we have so many different qualities where each person can give what they have to the team.
"I think it's really important to have a strong captain but there are also people outside of our leadership group like Papa [Sokratis], like David Luiz, who have gone through a lot and have so much experience. When they raise their voice, they're listened to as much as the leadership group are.
"That's more important than anything else. Sometimes it's not just about having that one figure, it's about everyone in the dressing room respecting each other, listening to each other and moving forward in the same direction. That's what we've got here at Arsenal."