Lots of numbers begin thrown around, some of which seem reasonable and others not so much. But with no information about OPs experience, his game selection, his track record or the size of his bankroll, its important to begin with the basics, which are:
1) The purpose of a bankroll is to protect a winning player from undesirable large swings forcing them to move down or from "going broke" and not being able to play any more.
2) From point 1) follow, that its not possible to have a bankroll, unless you are a winning player in the games you play.
3) From point 2) follow, that you need some sort of track record to suggest, you are winning, before it makes sense to talk about bankroll management. Until you have such a track record, you should think about a poker budget rather than a bankroll. Like maybe deposit $50, every time you get a paycheck, and then dont deposit again before the next paycheck. Or whatever your financial situation allow.
4) You dont need a bankroll, if you are mostly playing poker for fun. Make a poker budget instead and just play whatever games give you the most fun.
5) It makes no sense trying to manage some random very small amount of money in a poker account as a "bankroll", since you can just deposit more, so losing it does not mean, you need to move down or stop playing.
6) Being overly conservative with a small bankroll will hold you back and prevent you from moving up and winning some
real money. Or from having more fun, if point 4) apply.
I hope, this helps.