To the OP--the spinning workout you described is moderate intensity interval work, not HIIT. HIIT is a specific protocol of 5 to 10 minutes of sprints, like 8sec sprint/12 sec recovery up to about 15sec sprint, 45sec recovery. Some do 30sec/60sec, too. Then you can follow this up with 10 more minutes of lighter intensity steady state cardio to help burn off the fatty acids you've freed up with the intervals. Add a 5 minute warmup and 5min cooldown, and there's your workout.
Nothing wrong with your spinning if you like it! It's all about burning calories.
As for how many carbs you'd need, this is soooo individual. Really, endurance cardio like marathon running (not sprinting or competitive cycling) and low rep, high weight resistance training are not big glycogen hogs, so high levels of carbs are not needed. Maybe 5 to 50gC around the session, something you have to play with and see what you need.
Sprinting, other forms of HIIT, and higher repetition/lower weight resistance training (depletion style) will use more glycogen, so will need more carbs. Again, how many more will depend on the individual and their intensity.
Iluvgreys, you might want to check out the link in my sig to "My other home", a forum dedicated to women who are interested in weight training and low carbing. Joooolia is a member there, so it can't be all that scary,