I just want to say, I use the business card "method", from time to time, and my family teased me for it and some reddit feedback has told me it's the wrong move, so I appreciate seeing how the story played out with that!

I do it for the exact same reason - I don't want to put someone on the spot for their information, and I'm proud of my business (even though it is very very small) that they can verify and get to know me by looking at my website or social media.

And I only do this when I've had a good dialogue with someone! I've never handed them out as a chat up line, only once we've talked a bit.

Plus I figure when it's the right person, they won't care either way and just be happy to have my number! All it takes is one.