blueman wrote:

Any suggestions on type of glue and technique for bonding PLEXIGLASS
to clear, smooth POLYETHYLENE?

You're going to need an adhesive specifically designed for low surface energy
plastics. These are not cheap. There are some made by Loctite and 3M among
others. They are usually called structural adhesives and one example is 3M™
Scotch-Weld™ Structural Plastic Adhesive DP8010. You won't find this stuff in
your friendly neighbourhood hardware store - it is only available from adhesives
suppliers and a few specialty shops.

Do a web search on "polyethylene adhesive" and see what you find.

Mike