lol
you got the newguy jitters
with bjj, you're supposed to rely on technique first, and strength/speed/other athletic traits last. I used to get winded because I would end up just wrestling guys and using strength and speed to get out of positions and holds. In the end, I would end up with my body flat on the ground (a no-no), defenseless and tired. That usually led to easy submissions. As I started rolling more, I would get tips from coaches such as holding a position and breathing. If you forget to breathe or work too much when you should not, you'll gas. Always remember to move when your opponent moves. Until then, you can hold on as long as you want.
Until they start throwing strikes....then that's where you get more into combatives or mma-type jiu jitsu.
if you're really serious tho, you'll start doing more muscle-endurance exercises like plate/kettlebell circuits, so you can have more stamina. Straight cardio such as running is good, but it doesn't really all the muscles you need for grappling.