Is there a way to link only one Pressero asset(that update regularly as base artwork) to one edoc template so that once user customise this product they only see the specific asset image not all other asset images ?

Answer:  There is no direct way to achieve this as once you allow the users to upload the image from assets only it will show all the associated asset images in the selection however there is a workaround that could be helpful in this case.
For Example:

Let's say you have 20 different assets in Pressero and you would need to link them to 20 different edoc templates.
Within Pressero you can create 20 different categories for each asset and assign each asset to the associated categories in the below manner.
Asset 1- Category 1
Asset 2- Category 2
Asset 20- Category 20
Within eDocBuilder If you are using Form Based Type template than via either Standard Image Upload or Advance Image Upload you get an option of "Allow upload from assets only" in the data capture tab for an image field.
In the same section you also gets an option of "Initial asset category"
You can paste the name of the initial category here originating from Pressero Asset Categories for each edoc template in an image field.
By doing so once user customises this edoc product on a pressero website ,the template containing image field will only allow the user to upload asset from the specific category(that will have just one single asset not all the asset images).