best way to build a Bankroll with 10$

[ChipFish]

If you are asking a question like this when you have a bankroll of $10 you are in serious trouble.
Your best bet if you are seriously thinking of playing tourneys with a $10 bankroll should be to get into the highest limit game you can, and playing the first hand all-in.
Actually, an even better idea, would be to take the first quarter you find on the street, and put it into a slot machine. You'll have better odds to win then playing tourneys with that roll.

Brian actually gave you some good advice.
You have 3 options...
1 Take the advice and grind out a bankroll.
2 Save some money until you have a decent deposit to take advantage of first deposit bonuses.
3. Do it your way and go broke on the same day.

Good luck. You are going to need it.