Something like saddle soap might work. Ask your local saddler.
A visit to a Saddle is a good idea. I have used Saddle Soap as recommended on my water damaged Luggage Straps. It did bring them up well after several applications.
The downside was that during the next downpour, the impregnated soap frothed up, washed off and I was back to square one
.
It is easy to re do Luggage Straps as they come off after each trip. A Bonnet Strap need something more durable, I would have thought.
If you quote this tale to the saddler, they may recommend a better product.
