Only Allow Bids from Authenticated Members

You can't do this within My Products, but you can if you export your products from MP, edit in spreadsheet, then re-import.

I could do that in about 2 mins.

See the guide here..

CSV Export - edit - import - Bulk update. How to guide. – Help - Trade Me

I know Gary has given you a good answer, but for an idea outside the box why restrict yourself to only some buyers?

I ran some tests a few years back and there was NO MATERIAL DIFFERENCE in the rates of failed trades whether a buyer was authenticated or not. 

I'd just leave it unticked, then monitor sales and fails. You might decide it's better to leave it unticked. 

Even if it was a heavy factor in fails, the maths just doesn't stack up.

This is super simplified but imagine:

Option 1. Unticked: Item in front of 100 people. 50 sales. 2 fails Total profit $48

Option 2. Ticked: Item in front of 50 people. 25 sales. 0 fail Total profit $25

Thank you

I just had a few $1 Reserve auctions this week - it tends to attract difficult customers.  All good, thanks for your feedback :)