Do I just need a provider to vouch for me? Is one enough

Not all providers use the TER white list system, nor is it to be used as a replacement for "traditional screening."
Even if you have white list referrals, most providers will still require provider references and prefer speaking with another provider, whether it be via email or phone.

Thanks

you have to ask the provider.  For some, one may be enough, but they will still do their own type of screening on you.  For most, if they use the whitelist as a part of their screening, they will probably want more than one, IMHO.  Remember, not all providers place much stock in the whitelist referrals.

...Some providers will whitelist a hobbyist on their own, sometimes without even telling him.  Some providers will ask a hobbyist if they can whitelist him.  Once in a while, a provider will whitelist a hobbyist even though she has never seen him.  GaGambler has posted that a provider whitelisted him even though he only met her at a Meet & Greet.

The reason some providers don't place much stock in the whitelist is because some hobbyists ask for them and the providers feel pressured to give them.  Some providers will also whitelist a hobbyist in exchange for a good review.

Finally, there is one voluminously reviewed provider who whitelists everyone she sees.  I believe this is because if you write a review of her and you DON'T get a whitelisting, it means your review is fake.  Good way to keep track.

asking her.  BPS, while it may happen, I doubt that it's as widespread as you seem to think it is.  I won't say it doesn't happen, but I don't think it's the norm.