Unicorn here. Have been following this thread with interest Mr. and Mrs. UC. I do not know how all single fems feel but I would to step in with a few notes from my position. First off, what Mr Fun says is on the money with regards to profiles. It helps if the unicorn senses she will be regarded as desired or wanted by both of you for being herself, not just because she is one. The unicorn has plenty of options to just be a toy or lay in the swing world. But if you want to go from chasing to catching, you may be best served by helping her want to come to you over all the other contacts she receives. While the "His answer" gives the unicorn something to tie into, the "Her answer" says it can be any one....just a body that fits some undefined physical parameter.
Tybee brings up another very good point. Mrs. UC, you may quite well not be a passive woman. But giving the impression in person, or online, of being passive will cause me to react as Tybee does. Passivity has led to feelings of wife is doing this for hubby, wife almost laying there with me doing most of the work, wife getting uncomfortable in playtime, me being an extra and not an equal part of the "romp". All of which has proven out. Plus, for me it is difficult to get excited about being with a couple when the sexual energy and overatures are only coming from one person. I clearly do not know you well enough to say whether you are passive or not. Nor do I know how you would be in a threesome sexually. But I can say, your chances of catching one or many unicorns increases if you make her feel you desire her.
Practice letting Mr. UC start the in person conversation, or the email chats, or IMs, etc. to get the ball rolling but you jump in quickly. Become a part of it. Then 50% of the conversation. Then more. Until you can make those overatures on your own. If the idea is for you all to play as a threesome, then you need to show her who you are as well as who your husband is. It is both of you she needs to feel desired by. And if it is for him to watch and you and she to play, then by all means...it all needs to come from you. Lean on him but push yourself to not appear passive, sure of what you are looking for, and why the two of you could be the best contact a unicorn could make.