I started using inkbrush in Splatoon 3 (originally an Octobrush main) and what I find helpful is using the roll mode (holding down the shoot button) to psyche out people shooting at you. Your movement speed in roll mode is pretty hard to contest.

Running sub saver (if you’re using the vanilla brush) also helps a lot too so you can throw bombs without using all of your ink. That way, you could roll a bomb on the ground, move in with your brush, and pressure them on both ends.