Booking Templates are by default shared at company account level. This means that everyone, including Suppliers, can see these templates.
However, Booking templates, can be restricted to a certain group of users (or suppliers, for example)
To assign a Booking Template to a specific supplier, simply go in the booking template you want to edit from the Booking Template section of your account, and set it as Restricted and select the user you want to share it with.
Once done, click on Save. This will update immediately your Booking Template