Do you have a picture of your bridkle? Most bridles can be adjusted to carry either a curb or a snaffle.
A few different snaffles:
Single jointed eggbut. Most common, and I would guess cheapest if you are strapped for cash. Some horses don't like these though, because they have only one join, they can 'nutcracker' causing the join to hit the roof of the mouth. My little arab is quite happy in this bit. The eggbut sides don't pinch.
If she is having issues understanding turning, something like a D ring might be better. The straight side of the D puts pressure on the side of her mouth when asked to turn, re-enforcing the turning aid.
A loose ring gives the bit more 'movement' and allows the horse to have some play if they like it. Only issue is sometimes they can pinch.
The most 'favoured' snaffle would be a double jointed snaffle. The two joins in the middle eliminate the nutcracker effect of a single join. You can get a double jointed snaffle in any of the cheeckpieces above, eggbut, loose ring, D ring, etc. This si the bit I use on my main horse, a double jointed loose ring snaffle. This one has sweet iron and copper to make it more 'tasty', mine is full copper.