How much of my roster budget should I leave open after FA for promotion bonuses and whatnot? 

If you wait until the end of the season to do your promotions the cost is negated altogether.

Even if you planned very poorly and found yourself having to promote 20 guys from each level (a very exaggerated figure) during ST or early in the season, it would cost less than 1M.

If you have guys that you will be calling up after day 20 they generally cost around 250K per player added to BL squad. Additionally I like to have a little cushion for potential trade options during the season.

I try to keep between 1M and 2M, depending on how many BL promotions I have planned on for that season, but always try to keep a minimum of 500K or so on hand in case of injury at the BL level which may require calling up a AAA guy to fill in, the cost of which is 250K-ish depending on how deep into the season the injury occurs.

1-2m is about right.   But, if you end of with 5m, don't rush to spend it.   Waiver claims or a trade could eat that up pretty quickly.

Great, thanks.