One of my players is asking about starting his new character as an initiate. I was wondering if anyone out there had a house rule they used for this, and the BP costs they apply...

use karma built system, problem solved?

Rest of group is built using BP system (it's a character to replace a gnome rigger who was in a horrendous car crash just after spending his last point of Edge...) so I don't want to use the Karma system. Good call, though.

there was some way to translate BP to Karma, but i can't find it right now, as i am at work

The rule of thumb is 1 BP = 2 Karma, so you could use that.
Though, the main reason against letting people start initiated is that due to the costs (however those are paid) the char is almost guranteed to be a one trick pony at best, so it's usually better to give him a shot at a magical group of his choice at startup and let him use the first karma points to actually initiate.

Not really, if your using karmagen

1 Build Point is generally worth 1.5 Karma. You can use that conversion, or simply go with 5 + (5 x Grade) BP - this results in it costing a bit more, but that should not be an issue. It also strongly discourages starting at Grade 5 or higher, without strictly disallowing it.
Quick breakdown of the total cost for each Grade:
1 - 10 BP
2 - 25 BP
3 - 45 BP
4 - 70 BP
5 - 100 BP

I also suggest disallowing Group or Ordeal discounts during character generation, & charging 5 BP to be a member of a magical group.

Sure, using the base 750 karma point system, you'd have no problem to pay for that. You'd have no problem to pay for most stuff, given that you're somewhere around 50-100 points of karma ahead of a regular BP char already.

Still, for a magician BPs are already hard to come by, so paying a further 30 points or so hurts your versatility.
At least as long as you don't start as a grade 1 initiate with magic 6 and convince your GM that your 6th point of magic should only cost you 10 BPs, as it's technically not your maximum anymore. That way you're actually coming out ahead...

150, actually.

Of course, you do need to pay for Knowledge skills, so maybe 125.

BP system, so the cost structure has to be linear. How you got to your grade is irrelevant.

If you charge 5 BP per grade, on top of arcana, you should be good to go. From my experience, the fair cost comparision is that to fully rebated initiations, or 7/9/11 karma. A cap to grade 3 would IMO be wise, as well as keeping the magic 6 - limit for chargen. Those who are loners will pay enough for their inefficient decision, some chargen leg-up is acceptable.