Re: To double or not?
If she is shy, you need to show the initiative, its very important, push the boundary a little and then bring it back a notch so you catch her off guard, but let her know you won't keep pushing if she tells you to stop, be it a hug, a kiss or sex.
Now, as far as the date or it being awkward, NEVER acknowledge that she is awkward, it will put emphasis on that and you DO NOT want that. I would try to go out on a date with just the two of you. The KEY and SECRET to getting rid of awkwardness is to be comfortable. You don't have to be comfortable, but you need to act the part. I'm always nervous when I go out, but I maintain an image of being comfortable and it never fails, at the very least they will tell me how comfortable I make them feel.
Remember, it is natural for her to mirror your emotions if there is a connection, so if you are comfortable, she will be comfortable by default.
KISS - Keep it Stupid Simple