Offering to pick her up is completely unnecessary and probably sets off a tiny red flag. Women like their own wheels.
Effusive apologies work against you. As charming as your note was it keeps the mistake highlighted.
Going into a home is very personal. Keep the surroundings impersonal.. movie theater, coffee shop, light and easy. No one feels trapped.
It's not her loss, it's not your loss. It's a learning experience. Find what works. Don't do it all. And realize your limits. Postponing a get together is okay. Just be upfront about it. Simple statement.
