This woman expected a hot guy (likely would be called a 'Chad') to initiate a conversation with her and ask for her contact info. If a hot guy is expected to start interactions, more average guys will also have to face the reality of that expectation.
Women in general still expect men to ask for the first date and/or contact info.
It's possible a 'Chad' could get away with handing out a business card and get some nibbles. However, most men with Chad tier looks are confident enough to ask a woman to meet him for drinks at a bar and collect her phone number if she agrees.
The card idea is an old idea that has been tried in field before and has failed.
This is a socially stunted solution that isn't really a solution, even in the specific setting of a speed dating event.
First off, if you value yourself, you do not market/sell yourself at speed dating. Speed dating is dog crap quality. Luxury brands don't sell at 7-Eleven. A guy who realizes that he has any sort of value isn't going to speed dating. Speed dating is dog crap quality on both the male and female sides. Females who realize their own value also won't go there.
That speed dating event had an odd format that most speed dating events don't have. All you've done is tried to create a solution for an unusual speed dating format. In that unusual speed dating format, the expectation would be for men to initiate contact and further the interaction.
The use of a memory jogging card isn't going to help women contact you.
You are not getting mocked. This is fishermen telling you which tactics work for catching fish. We're giving you the feedback you need to improve. Plenty of men have already field tested that card idea going back 10-20 years or longer.