There are a couple of ways. One is to add in a backslash before the space, which tells bash to include the space as part of the name. The other (much easier, but not useful for scripting) is to change to the directory, then type 'cd' and the first part of the name, and hit the 'Tab' key.
The tab key will expand the name of the directory for you, and save you a lot of typing. If there are two or more similar names, hit tab again to see a list of them. This is a good thing to remember, write it down even, because it not only works with bash, but a lot of command line programs use it as well, and it will save you a ton of typing over the years--and allow you to use more descriptive names, not short ones that are easy to type, but cryptic. Naturally, tab can only expand exact matches, so remember that Linux filenames are case sensitive.
An example of how I'd type something similar (and no laughing from those of you who know other shortcuts--we don't want to confuse the newbie
The keypresses(don't include the <>):
This will look like:
cd /home/myfiles/windows/Program\ Files/bug
cd /home/myfiles/windows/Program\ Files/bug-ridden
The reason I typed a few letters in some of the places was to narrow down the number of similar files. For instance, typing 'win' instead of just 'w' means you won't get other w words. If there are a ton of similar names, typing tab twice at the same places will give you a list.
Hope this helps, and don't worry about asking too many questions. Sometimes a "dumb" question can net you some really useful stuff.