A lot of women don't lift weights because they think they will "bulk" up. This isn't true. Don't let this discourage you from getting in shape.
The idea behind a triathlon is biking uses your quads (front of legs), running uses hamstrings (back of legs) and swimming is upper body. So yes, running and cycling are complimentary if you don't overdo it.
You should be careful not to overtrain, but I would also be concerned about you burning out. It's better to be excited about a bike ride, than starting to dread it. Make sure you keep it fun.
"Well-behaved women seldom make history." --Laurel Thatcher Ulrich
'09 Trek WSD 2.1 with a Brooks B-68 saddle
'11 Trek WSD Madone 5.2 with Brooks B-17