One thing that helps me with bunny hops, is that I learned to fall gently. I am now completely unafraid of falling on the ice in any direction from roughly standing height. So I'm not afraid to commit to the jump. I can go as far as I can onto the toe pick, and use the leg swing to pull myself high into the air, without fear. I wouldn't have been able to do that if I was still afraid of falling. Of course, if you are taking group lessons, the extent to which your coach will show you how to fall gently depends on the coach. Most spend very little time on falling.
As others have indicated, while there might be a time when the blades limit you, at your level, you are much more likely to be skill, practice and fear limited. More practice time, on uncrowded ice if you can get it, and more instruction, are a better investment. But if there is a problem with your boots - if you aren't in them snugly enough, or they don't support your ankles, that could create an injury. Especially if you don't fall right, or if you fight a fall too hard.
If I were you I wouldn't go to the top end freestyle blades, even if you can afford them. Because it takes time to get over that super-aggressive toe pick, if you ever do. The chances are, if you aren't getting very far off the ice in your bunny hop (though, BTW, a lot of people don't get very far off the ice in bunny hops, and you probably don't need to get very high to "pass"), you are probably still a bit timid about using the toe pick and the leg swing. A super-aggressive toepick would just make that harder, because you will sometimes jam into the toe pick before you are ready to jump.