I bought a bike from an individual who didn't meet me at his house... I think he wrote his name down, but it was something like "Smith". I still wonder if the bike was "legit", or if there was a reason the seller provided minimal info.
As far as meeting as soon as possible. Hot items disappear quickly. You snooze, you loose. And, I've had sellers state that they would hold an item... then sell it out from under me.
A phone number is nice, and I like to exchange the number before heading to see something, just in case I'm late, get lost, or something comes up for either person. Are there people without cell phones?
Say you choose to meet in the local grocery store parking lot, have say $50 worth of misc bike parts in your vehicle. Is there any more risk to you than the person who wheels out a shopping cart with $100 worth of groceries?
Now, you might not want to let one of these mystery buyers do a test-ride of your $5000 bike and get out of your sight. And, only meet one at a time, not a group of 5 or 6. Perhaps verify who you are meeting in the communication. Husband, Wife, Kid, Mechanic, ... Not the crowd of neighborhood goons.