I\'m attempting to get into the directory /cygdrive/c/Users/my dir/Documents:
$ DOCS=\"/cygdrive/c/Users/my\\ dir/Documents\"
$ echo $DOCS
/cyg
As an alternative to using quotes, for a directory you want to go to often, you could use the cdable_vars shell option:
shopt -s cdable_vars
docs='/cygdrive/c/Users/my dir/Documents'
Now, to change into that directory from anywhere, you can use
cd docs
and the shell will indicate which directory it changed to:
$ cd docs
/cygdrive/c/Users/my dir/Documents