Recommendations for bridge muting material

Thick dense foam (ie, door) weatherstripping would do it, and is conveniently adhesive on one side, just layer until you get the necessary height. It's usually the darker grey or black stuff, the light grey or other light colors are not dense enough.

 

Try experimenting with a small roll of cloth, like terrycloth that towels and washcloths are made of. Make a little roll, holding it together with a couple loops of string. Make it a diameter that slips between the strings and the body and stays in there by light friction. Then play around with the position of it; how close to the bridge it is. You'll probably find that moving the position of the roll will be a better way to adjust the damping effect than trying to work with the stiffness of the roll.

 

This is what I generally use. I am currently using a "chore boy" dish sponge cut to size. I have been considering installing the felt mutes that came with my avri j bass. Has anyone used these?

 

I like gardener's kneeler pad foam.

 

Weather stripping, a velcro strap cut to size, and industrial strength velcro on bass (comes off without damage if ever needed). Then it can be removed between or during songs. I remove one side and just let it hang. Total cost is about $12 in home Depot, but you can make about 6 of them with those materials.