do NOT play $1.2 sngs on stars. The rake is horrible.
Let exclude skill factor for now and view the sng payout structure itself.
If you play 9-player sngs 9 times, by regular probability, you'll win each places one time. Total Prizepool is $9. If you bought in 9 times, you have paid $10.80. So overall, you're paying the site $1.80 for every 9 games you play, thus, paying 1.5 times more than the buy-in. So even if you're extremely skilled, your edge to profit is very small.
You're honestly better off just gambling it up with $2.25 sngs.
If you're really serious about Bankroll Management, play $1.1 DoN. Rake is average and your skill edge will pay off better than $1.2 sngs.
As TPC said, $20 isn't even a bankroll unless you're on full tilt where you can mass table and grind 30 cent satellites.
And you can't really apply bankroll management with $20 because you cannot move down when things are going bad. All you can do at this point is stick with a stake and just keep playing until your bankroll either flourishes or goes broke. Once your bankroll flourished, then consider bankroll management.