Both ladies have given excellent advice and pointed out some great items.
Wahine is correct in stating that you want a bike that is enjoyable and easy to ride. If you have to work really hard to ride it, it's not fun. The Trek 1000 is a good starter bike, but if she gets serious about cycling/tri's... it will be gone in a year.
The components on the bike are important... good components = easier shifting... and a more enjoyable ride. For her first bike Shimano 105's will be just fine.
Now... I would like to add... that she needs to be FIT to ANY bike you want to purchase for her. It's very important that the fit is correct, or she will be miserable riding the bike.
With that said, it's probably not a wise idea to just go pick out any bike and surprise her with it. It hasn't been fit to her.
You are so very sweet to want to surprise her... but she probably needs to be around when you buy the bike. Maybe you can get her a gift certficate to a bike shop... that way you set the spending limit... and she gets to pick out her bike.
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"