Buying a bridle which gives many bitless options seems to be a really good idea. You can try the different options to see how your horse likes each one and then as you progress you can even then have the option to try a different type. There are a few out there and I shall incude the most popular ones below but there are probably more.
Micklem multi-bridle.
As you can see these are a bit different shape to traditional bridles. Izzy here was trying mine to see how it fit and if she might like it. I have found that the sizing isnt quite the same as traditional bridles and the fit can be hit or miss. They seem to either fit well or not at all.
Looking at the above you could attach the reins to the D on the side of the nose giving a sidecue effect, the D rings are slightly further towards the middle of the nose than some sidecue noses.
The bridle comes with a webbing long strap which attaches in a figure of 8 type shape to make a cross under style and theres also a chin attachment to create a scawbrigg type bridle.
I did find that although Ive worked to supple the leather it still wasnt quite as soft or supple as I would ideally like.
Here is the same bridle on Sally, Ive needed a longer brow for her but we managed a decent fit. You can also see that I have put the reins on the little Ds which were designed to attach the bit to. Ive also added a fleece noseband cover. Sally actually found this set up quite comfortable, acceptable and she responded quite nicely. When we found this was working I decided to have a similar brile made in beta biothane as pictured below.
The photo does make it look as though the chin strap is quite tight, howver it wasnt and Sally really wouldnt have liked it to be tight!
Matrix bridle.
This has many options of various types of bitless. Ill put a link for you to a website selling it so you can look through it at leisure. It really does have a lot of options, suitable for use with several horses or for trying different types yourself. There are also other types on the webpage for more pics/info.