I have a funny feeling that you need to go with a much higher quantity to have cheap logo'd sticks. However, once you get past a certain number, the price goes down significantly. While I have never enquired about printed sticks, I am quite well-versed in printed items.
I would try 100 pair of cheapie throw aways and 20 pair of good ones for your initial order. Your price would be cheaper per pair, for certain. Also, remember that you need camera-ready art, and the set-up will be expensive at the outlay.
How do you want it printed? "burnt" in? Paint? Ink? All of these things contribute to price. Maybe someone else on the forum has done this. It's not for the $100 per band member gigs, for certain.
If it were me, I would buy up every "20 pair of sticks for $5" bag (a bit of an exaggeration, perhaps) at Banjo Center you can buy at those big sales and see if someone local could print them up. Just a suggestion.
Good luck.