If your intention is to have your "personal card" available as a kind of "business card" to easily share with your partners, there might be a much better idea than exporting it as vCard: Export it as QR-Code. So you only need to display that QR-Code on your device, and your partner can use a QR reader to "snap" it. It would then be detected as a "business card" (actually, the QR Code will represent a vCard -- AFAIK even in vCard format), and so your partner can directly import it into his/her contacts.
How to do that? An app I started using a while ago is QR Droid. It comes with some pretty practical widgets offering shortcuts, and has several add-ons on the playstore for sharing your current GPS position as QR Code, and more... OK, back to topic:
QR Droid "business cards", history, selection to create a code (source: Google Play; click images to enlarge)
As the screenshots show, this app is able to create "business card QR-Codes". You can even edit them (e.g. embed an image into the code to make it nicer looking). To show it to your partner for scanning, you can easily pick it from the history (second screenshot). And as a side-effect, it can do much more -- not only create, but also read QR Codes.
PS: As the contact will be exported as vCard, you can also share it with your other devices this way. It might not be imported to your "personal contact" on the other devices, though...