To be blunt, poly is inherently awkward. It's just full of weird and odd conversations you never thought you would have. (For instance, I just told Whip (my partner) that I was excited about an upcoming date. The date is not with him. Not a conversation monogamous folks have.) Dating is basically awkward and odd in general. But with poly, there is the addional layer that there are few conventions and traditions to rely upon. One has to make it as one goes along. While exciting and interesting, it can also be uncomfortable. So, welcome to the land of awkward conversations and no road maps! (Really, it's fun!)
Also, you will be rejected. The only way not to be rejected is to not look for other partners. (And you will do some rejecting too.) Anyone who makes an effort to date gets rejected. Accept that now. Learn to be rejected gracefully. Learn to decline others gently and clearly. If you don't want to be rejected - and you prefer not to face this aspect of yourself - I gently suggest don't try poly. (It is possible to be the monogamous partner of a poly person.)
You will not be everyone's cup of tea. Many women (assuming you are a straight man) are just not going to be into a married man. Your experience of your wife finding it easier to date and find partners is pretty common.
I suggest being upfront about your situation. Something along the lines of 'My wife and I are polyamorous. [Insert brief definition here] She is dating and has a boyfriend. I date too. I think you are really interesting and would lke to ask you out on a date.' It is definitely a weird conversation to have. But I personally like to have things clear.
There is a LOT here about dating, about how to have those odd conversations. Try searching for 'dating' and similar words in a tag search. I also suggest just wandering about on the board, read what interests you. Good luck!