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As far as bankroll management goes, if I decide to sit with a 50BB stack, would it be ok to jump up to the next highest game?

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hm, bankroll management discussion is tricky. here are my thoughts, but I'll give fair warning that this is just an inkling and has not been mathematically verified.

Playing a $100 stack in a $1-$2 game will still be lower variance than playing a larger stack in a $1-$2 game.

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I think you can verify it with the Kelly Criterion.

Assume Player A buys in for 60xBB in a 5-10 NL game, and wins +1500 in his winning sessions and loses -800 in his losing sessions. He wins 55% of his sessions, in part because he doesn't chase his losers. So he doesn't dig himself out of a hole that often.

Kelly would say he gives 1500:800 or 1.88:1 odds to himself every time he sits down. And he wins 55% of his gambles. So, 1.88*55 - 45 / 1.88 = 31.1%. His average loss (ie the amount he risks when he sits down) should be 31.1% under Kelly. So, bankroll = $2572.

Player B buys in for 1500 in the 5-10 game. His average win is +3500, but he chases losers to get even and sometimes sustains large losses. His average loss is -2500. He wins 60% of sessions. He gives himself 1.4:1 odds. 1.4x60 - 40 / 1.4 = 31.4%. So, 2500 = 31.4% of bankroll, or bankroll = $7962.

Of course, full Kelly has 13.5% risk of ruin if you don't drop down in levels. If you are unwilling to go to smaller games, better to operate at quarter Kelly, with 0.03% risk of ruin.

Player A quarter Kelly bankroll = 10,288
Player B = 31,848

Player B wins more often than Player A (60% to 55%), and the difference between Player B's winning and losing sessions is greater ($1000 to $700). Over time, Player B rates to win more money.

But Player B needs a bigger bankroll because of the bigger variance. More succinctly, he simply risks more on each gamble, which in turn impacts the odds he gives himself every time he sits down.