Hi Harold and thanks for the great questions. First, asparagus does spread but not very quickly in most soils. If it loves the location it could spread out to cover twice the area it originally covered in a few years but in  my raised bed garden the asparagus has not spread at all --- we do have cool summer weather so that must keep it's growth in check. As for a rubber mulch around edibles I have not seen any studies that prove the rubber would be harmful but to erase any doubt just use a mulch of newspaper or cardboard or better yet wood chips instead. An organic mulch like wood chips will improve your soil over time as the wood begins to rot and decompose. Finally, using a thick layer of newspaper around plants then a mulch or covering of bark or wood chips on top of the paper is a great way to smother and keep out weeds and can be used anytime of the year that the ground is not frozen. Spring is a good time as the wet weather will help to weigh down the newspaper and help it to meld to the soil and keep new weeds from sprouting by blocking all sunlight while blocking wind blown weed seeds from landing on your soil and hiding among your plants. Keep growing, Marianne Binetti