Yes, and it's a good idea, too! I'm actually kind of a gym rat. My exercise routine has changed, though. Pre-transition (I'm mtf) it used to be about two-thirds weights and one-third cardiovascular (treadmill, ellipticals, stairclimbers, etc.). Now that's about reversed, more cardio than weights.
I hear you about not wanting to get "bulky." As an mtf, I don't want to look muscle-bound. Athletic and healthy, yes, but not bulging with muscle. That's why I have shifted the emphasis to cardio.
A strong cardio routine is great for your health. My resting heart rate is way down, which is good. Also, cardio helps to control blood pressure, which is sometimes problematic for folks on HRT.
See ya at the gym, richie!