Adam, I think you are just trying too hard, and care way too much what someone thinks. Try this. Tell yourself that you are only going to establish friendships, and strive for many good friendships. It is a much better way to get to know someone, and as you get to know them, if the Lord intends things to develop further, they will, and that person will love you for the beautiful friendship they had with you before it became about more.
I know when a man tries too hard, often I get uncomfortable with it. Just way too much pressure. So stop trying for the date, and just be interested and helpful. Genuinely want to get to know her, and don't make it about what she might think of you, for if you are genuine, and you have a heart for Christ, she will see that.
Don't make it one on one, make it a group and fun activity like a study group or getting involved with projects. No narrow focus on you or her, but a great opportunity to see who they are, and how they interact with everyone.
Try it and let us know how that works, and may God bless you along the journey.
I know a young man who came back from overseas with no legs below the knees. He found God --Love -- Marriage and Children. It took him a long while but he finally got the message from God.
This man then went on to defy what everyone said he could or could not do. Every day he tried to enjoy life as much as he could -- with a Spirit that everyone admired. We would go out and he would get all the attention. He did not try to impress anyone or attract attention to himself; he just was such a happy spirit and Fun to be around.
I don't know your situation, so I really can not be more specific, but somehoe you have to get people to "see" past your disablilty and see who you are.
Steven Hawkings (whom needs prayers for his soul) is argueably one of the most brilliant minds in the world today. He has wriiten books -- won awards -- is married and he is also severely challenged and needs a wheelchair.
I hope any of this helps. Keep praying for strength.
Peace
Develop success from failures. Discouragement and failure are two of the surest stepping stones to success.