Hi Shadow,
What I have found over the years is the more solids (white glue) in the mixture, the less it wants to mist from the nozzle, and the more it wants to "squirt" in a stream, as you are finding out. Your 50-50 glue/water mixture is way too strong to run through any spray bottle. You could probably alleviate this problem by using an industrial-sized airless paint sprayer, but that seems like it may be a bit of overkill.
For general scenery work, you want a maximum of about 15% glue in the mixture, the rest being water and a few drops of liquid dish soap. Or in other terms, about 1 part white glue to 5 parts water. This is about as stiff a mixture that I have found that will mist through a spray bottle. The nice thing about a spray bottle is, you can cover a large amount of area in very little time. I like to spray areas right before I go to bed, and let them dry overnight. Setting up a fan to circulate the air over the area will help speed up the drying time. Sometimes you may want to spray the area a second time, but I have found that once is usually enough.
Here's another tip: Elmer's white glue is soluble when dry, just wet it down again and it will soften up. Acrylic white glues (Mod Podge Matte Medium, etc.) are not, they are pretty much water-proof when dry. I build trees using Mod Podge, I don't want the foliage falling off if I come in later and do some more scenery work or re-work in an area. Or you may wish to use acrylic glues for ALL scenery on modular show layouts, so humidity, leaky roofs, spilled drinks, etc. or any other moisture problems don't do a number on your prized show module.
Hope this helps.