First, the disclaimer: Everyone's Mileage Varies
Here's a rule of thumb I've found works for me - I used it when I lost 50 lbs to get down to my current rate of 220 lbs - at 15 mph I believe I burn about 40 calories per mile or 10 calories per minute.
For your 7.5 mile ride, that comes to 300 calories. I've seen gym bikes, bike computer devices, etc say more like 450 as you saw - which is more like 900 calories per hour. But when I was really strictly logging the calories I ate and the exercise I did, I did *not* lose weight at a rate that the higher calorie burn would predict, came much closer to what the lower rate predicted.
I think the simple answer is always use the lower value if you are watching calories in order to lose/maintain weight. If you are not trying to control your weight, don't worry about calories burned.