Biking vs. Running

I have a huge block when it comes to running so I'm trying to work up to it by biking first. I've read that you need to bike 2x the amount you would running to get the same workout. SO monday I biked 8.4 miles which would then be equivalent to 4.2 miles, correct?

No - impossible to quantify. Compare the effort riding a heavy MTB on knobbly tyres against a fast, light, road bike on skinny slicks, the road bike would be almost twice as fast for same effort. You can use effort or time but not distance. Better off using a HRM for comparison.

Do you get about the same cardio as running with biking?

Yes to a large degree. I find my workouts are much more controllable on a bike but I'm also a crap runner. I didn't train for a 5k at all but on one of the rare occasions my knees didn't hurt I ran my first 5k for about 10 years in a reasonable time with no difficulty fitness-wise.

I also just joined a gym with a pool so hopefully I'll be adding swimming into the whole thing soon.

Sounds like a Triathlon would be a great long term goal.....

Cycling and running are two great forms of exercise that compliment one another. Don't compare them, there a too many factors...like the type of bike (as already mentioned), as well as terrain, expended effort, time spent, weather....