Some people use some of the fabrics in the quilt to make a pillow slip to go with the quilt and put the quilt in that to gift it.
There are many bag patterns out there to make something to put the quilt in. The key will be to make sure it is big enough and has heavy enough straps for the person to use after the fact. I searched for Large tote quilted bag pattern There are many free patterns out there like this one
http://blog.missouriquiltco.com/a-pa...g-as-promised/