I'm very sorry to say this, and I actually would rather not do this, but I almost agree with The Situation on this one, except "weak" isn't the right term. Feeling dizzy or feeling like passing out may not be due to poor CV fitness, but lack of proper breathing. But it's probably both for you, considerng you feel dizzy from some light aerobic work like biking.
Either you have a congenital problem, or purposely choose not to assess CV fitness by the following means
1. Reducing rest periods in between sets
2. Alternating exercises back to back
I used to do this due to the religious fear of hypertrophy. But it won't really cause you to gain as much mass as you think, most of it will be due to enhaned glycogen stores and water weight, which you can burn off from taking a few extra days off.
Squatting frequently won't make you any more cardiovascularly fit than simply doing some box jumps in between squats, or doing like 7 pushups after deadlifts, although for a primary strength exercise its better to focus on that entirely and reduce the rest period.
For myself, deadlifting heavy, and combining some upperbody strength exercises like pullups and bench, has made my heart much stronger, and it carries over to other tasks such as swimming, which my lungs would not be able to handle after just 1 lap. And I did not gain much muscle mass from doing that upperbody wise, in fact I gained almost none. Dips are another good way to get the HR up without gaining much mass. You're no where near your limit. You're no where near to even starting to create the adaptations necessary for CV fitness.
