The 24-year-old winger played a key role in the Eagles' promotion campaign last season but missed the start of the current season due to a hamstring injury.
He has featured in Palace's last four matches after returning to full fitness and is now targeting a second victory of the season against Everton at Selhurst Park.
"It will be a very tough game," Bolasie said. "Roberto Martinez has got them playing very good football.
"They've always been a good team and they've always worked hard, but they've added that footballing style to their game now, which will make it tough for us.
"I always want to test myself against the best and right now Leighton is up there with Ashley Cole as one of the best full-backs in England.
"I'll be looking forward to that battle because I want to prove to people that I can cut it in the Premier League.
"I think I've adjusted to this division okay. I'm still excited - when I come out on the pitch I'm sometimes too excited maybe, but I'm calming down now and that will help my game hopefully.
"It's always a dream whenever I get a chance to enter the pitch in the Premier League.
"That's the dream for every footballer, but I also look at it as a great achievement and I want to be here to stay, so hopefully we can stay up."