Everyone has given you great advice.

Since you asked specifically, and I didn't notice an answer, if you decide to continue feeding your BP outside its enclosure, it is probably better to put the BP in the feeding area, then add the mouse. BPs are ambush hunters, so this would be a closer approximation to the BP laying in wait and a mouse coming along.

That said, there really isn't need to feed her out of her enclosure. As has been said, if there is the smell of food on your hand or in the room, you need to be careful no matter what your feeding method. Otherwise, I suppose it is possible if the only time your snake sees your hand is feeding time, then it might make the association with food, but even if you don't handle your snake a lot, you should be getting in their enclosure to clean and give fresh water and such. So that should not be an issue.

There aren't very many people here who will try to talk you out of feeding live, so no need to worry about that! You are right that your snake is totally capable of taking down her own prey (and that includes stuff a lot bigger than little hoppers). The only real danger comes when it is not done properly. You do need to supervise the feeding; not necessarily watch every second, but just make sure the mouse or rat does get eaten. Never leave a live mouse or rat in with your snake. If the snake doesn't eat, take it back out.

A 4 month old BP eating only a mouse hopper every 5-6 days probably is hungry still. BP hatchlings can handle mouse hoppers for their first meal, and hopefully she's grown a lot since then. So, either switch her to bigger prey, or offer her a second one.

You definitely need to get her some hides. I'm not sure what kind of "dirt" is sold at a pet store, but more commonly recommended substrates for BPs are newspaper or aspen.