You could use a rubber curb chain cover, or you can buy leather curb 'chains' (contradiction in terms I know). There are also gel and sheepskin sleeves available (but remember to look for double bridle stuff as you won't find it for Kimblewicks).
S
Depending whether your bit has slots for the reins or not, you could use it without, lots of people do or just go to a mullen mouth snaffle unless it is the poll action you are after.