Herzlos

Everyone learns sometime. I've got a friend who was never taught by his parents for similar reasons and is now 37, he'll probably try and learn in a couple of years when his kids want to learn. Kudos for trying and opening yourself up to being a bit embarrassed. You'll get over it quickly enough and then never look back, and no-one you care about will make fun of you over it.

Have a look for local cycling charities (if you give us a location we may be able to offer something). There are a few near me (Glasgow, Scotland) that are all about getting folk on bikes and whilst they mostly deal with kids and disabilities I can't imagine they'd be anything but keen to help an adult learn. Some will have a dedicated track / practice space and a whole host of bikes for you try try with, and well as being able to provide tailored advice.

With a bike the propulsion is the easy part, and it's the balance that needs mastered (though complicated by the fact that balancing is easier as you go faster).

If you're getting help, then follow their advice.

If you're doing it alone, acquire a bike (anything will do) where you can sit on comfortably on the saddle with your feet on the ground, it'll likely be too small for 'proper cycling' but it's a start. Then focus on rolling down some gentle slopes with your feet off the ground until you're comfortable, then try some longer/steeper slopes and some turns. Once you're confident you're not going to fall overand die, try pedalling a bit whilst keeping the seat low so that you can put your feet down if you feel unstable.
Once you've mastered that, raise the seat up a bit and try to find a more comfortable cycling position (ideally your legs should be nearly straight when the pedal is at it's lowest point).

Then treat yourself to some beer/cake for achieving something a lot of people are afraid to do!