Using another ppc service along with AdWords
No, there's no reason why this wouldn't be allowed. Sending traffic to your site via AdWords or via Bing doesn't matter to either.
If you're asking whether it's OK to have AdSENSE on a page that you're advertising with AdWords, then the answer is YES. There is a problem there. If the purpose of your site is to display ads to earn revenue from the traffic that you send via AdWords, then you'll fall afoul of the arbitrage policy - https://support.google.com/adwordspolicy/answer/190442?hl=en
If you want to give a more concrete example, I'll be able to get more specific.
@Dave_Davis is correct and you can send traffic to your website from a wide variety of sources, without any problems. Google does not control or regulate advertising across the internet apart from their own AdWords program.
However, if what you're asking is if more than one active AdWords account can be sending traffic to your website at the same time (maybe from a campaign you're managing plus another campaign being managed by out outside agency, for example), then no, you are not allowed to do that.
Only one AdWords account should be used for one website.
There are exceptions of course. If you're interested, you can ask for details.
Google AdWords Top Contributor