Great question David. A few quick things:
1. Ask the parents before you ask the teenager, whether they'd mind you asking them. Explain what you'll be doing - getting to know them better, and reading the Bible together.
2. Don't put the teenager under any pressure - let them say 'no' without them feeling they've done anything wrong.
3. Meet somewhere where there are other people, but where you won't be overheard. A good place is in their home, in a room on your own but with the door open - or in a church room, again with the door open and someone around nearby.
4. Do it for a time-limited period (eg: a term, or six months). This helps ensure unhealthy links don't build, and sets expectations, and prevents rumours (or a simple feeling among the rest of the group that a particular individual is 'elite' or 'special')
5. Encourage church parents to be doing their own 1-2-1s with people!
Hope that's helpful?
Carl
David