I know what you are trying to say but it's not clear and will confuse many.
Your pricing is based on the competitor below you. If you are ranked 4th (ranking is based on your QS and bid), the competitor in 5th place (just below you) is the determining factor on what you pay.
Google has published the basic cost calculation. I'm sure Bing uses the same. There may be more to it but this is the essence:
cost = competitor ad rank / your QS
ad rank is QS times bid
If you play around with numbers, you can see how it affects your cost. The best way to protect yourself is improving your QS.
Less competition may mean lower costs. But all it takes is one to bid much higher than typical for a niche. If they happen to be the one below you on a consistent basis, it will affect your costs. I don't care if you're on Bing, Yahoo or Google, it will appear that it's higher on that platform. But the point as said is not which is cheapest.
Also, there are differences between platforms and you should try to exploit them. You may have a great campaign on Google producing different results on Bing and the reverse can be true. Think outside the box and optimize according to where your ads are showing.