Not being rude at all. You've got a life to live, and nobody should expect instant replies to texts. A 10-minute window is frankly unrealistic for most people who have jobs, errands, or are just doing something else. Responding when you get a chance is perfectly normal and healthy. The fact that you're thinking about this at all suggests you care about your friendship, which is what actually matters.
Your friend might be dealing with her own anxiety or attachment stuff, but that's not your responsibility to manage by sacrificing your peace. You could have a calm conversation with her about it - something like "I care about you, but I can't always reply instantly because I'm busy during the day. It doesn't mean anything about how I feel about our friendship." Set that boundary kindly but clearly. If she keeps pushing back or guilt-tripping you after that, that's her problem to work through, not yours to solve by jumping to your phone every time.
Most healthy friendships involve some back-and-forth timing where people reply when they're free. You don't owe anyone constant availability, even people close to you.