I've never wanted and thus never tried to make my living from poker, so I can't speak from that perspective. However, I do have experience starting small, mostly one-person businesses as well as training others to do so.
If we treat playing poker for a living as the business you're looking to start, then we look at the financial requirements in the same way. This involves not only working capital (bankroll), but overall financing.
One key element in this regard is to project how long it's likely to take to reach break-even after you pay yourself your monthly "salary". It would also be pretty standard to make not only a best guess projection but also to look at a pessimistic scenario.
So, using sample numbers, let's say your monthly living expenses total $3000. This means your breakeven is to win $3000 per month so that you can remove this amount from your roll while still having enough buyins.
Unless you can reasonably expect to win $3000 per month right away, you need to have enough money available to cover the expected shortfall while you work your way up to winning $3000.
Next, let's say you've decided $6000 is the minimum BR you should have, and also that you've projected you will win $1000 in month 1, and then increase that by $500 each month. This means it will take 5 months to reach $3000. During this time, your shortfall will total $5000, which means that to start, you need a total of $11k.
It's also a good idea to have more money available than you project because projections have a nasty habit of turning out to be optimistic, even the ones that are supposed to be pessimistic.