I wasn't 100% confident with my previous method.  I think it was a little too insulated.  Today I unwrapped it and reapplied the straw, leaving the top breathable.  The purpose of the plastic bag is to allow any rain to run off rather than soak the straw that is contacting the tree.  The bag was tore open at the top to allow the tree to breath.  The bucket is placed loosely on top.  It's not pretty.  Comments and suggestions are welcome.  I fear I may kill it with too much care.

Hey FF I dont know if I would use a plastic bag like that I would probably use a tarp the bag isn't going to breathe at all I know this because I have covered things outside not trees just random things for outside winter storage and some things got water logged from moisture. I know the top is opened but I would still use a tarp.

Anthony,

Thanks for your input.  Will the tarp let water in though?  That was my concern.  If the straw gets wet, then the wood may rot.  What do you think?

It might just a little bit I know when I use them at work like a roof so to speak to get out of the rain the only place it really ever leaks is the center where the water really builds up I personally have never seen anyone use a plastic bag the way you are all the old school Italians in my neighborhood always use tar paper and tarp and bucket no insulation etc first tar paper (roof paper) then tarp  then bucket with the top opened and the bucket covering the hole me personally I don't cover my trees or my dads when I first put some cuttings directly into the ground they where only just rooted when winter hit I was going to just put a 5 gallon bucket over them but didn't have the chance they all survived buried under snow and ice and are about 6-7 ft tall this yr first yr of growth and im not covering them this year either I wanna see what happens all the mother trees aren't covered ever so why not try it out I figure. Thats not to say if you have a warm weather tree not to cover it as soon as my starters grow the ones that need to be covered will be covered but if its a hardy tree I think you will be fine. Just get rid of the bag 

Thank you for elaborating.  I like the idea of just tar paper and a tarp.  Much appreciated!