Alright, let's look at the numbers:
The "bounty level" goes from 0 to 10, and goes up after doing a certain number of bounties - 2 each for the first 3 levels, 3 each for the next 4, and then 4, 5, and 6.
If the level is below 3, then all the bounties consist of low-grade pirate ships. At level 3 and beyond, you start to see the much-tougher "deserter" bounties.
The effective bounty level is the higher of the bounty level and a level based formula, which is:
(playerLevel - 10) / 3
This is rounded down. So, below level 13, it has no effect. At level 13, it's equivalent to you having done two bounties (but, note, since it picks the maximum it doesn't actually *stack* with you doing bounties). At level 16, 4. At level 19 is when you'd get to bounty level 3 and start seeing deserter bounties show up some of the time.
In addition, when posting new bounties, it'll always add a level 0 one if one isn't already posted, and one 2-4 bounty levels above the current bounty level, if one isn't already posted.
Maybe I'm wrong here, but it feels like up to level 19, anything you face should be quite beatable with either a combination of clunkers or a few decent ships - what you'd get from the profits of doing a few system bounties. Beyond that, the deserters, admittedly, can be pretty tough.
(I mean, I've played through a bounty hunting focused start a number of times, and it never stood out as being a problem, so that's a bit odd. I don't think my piloting skills are that good, which is why my inclination is to suspect something being confusing/misleading etc. E.G. trying to tackle the outlier high-level bounty without being ready for it will not end well.)
It does feel like this formula might be a tad aggressive, regardless. Let me tone it down to "(player level - 20) / 4)", so that the maximum bounty level you get from it is 5, at level 40.