Hey Jim, I'm assuming you're speaking of the four string F chord and not a six string barre chord. You most likely won't need the barre chord in bluegrass, so if you're having trouble barring the first and second srings at the first frets with your index finger, first try what Mike said, rotate your hand back (or down) to cause your finger to be flatter against the fretboard. If that still causes trouble, try the opposite and curl your wrist more in an upward manner (bringing your knuckles toward you) and try fretting both strings with the tip of your finger. If your fingers are big enough, this is very possible. So your wring finger is on the fourth string, third fret, middle finger on the third string second fret and your index finger fretting the first and second strings at the first fret.
On an A chord, it's usually taught to fret the second, third and fourth strings at the second fret with three individual fingers while still clearly playing the first and fifth strings open without muting anything. Yeah right, not if you have big fingers. Forget that if it's just nearly impossible and use two fingers to fret the three strings (I use my index finger on the fourth string and let the back side of it touch the third string and my middle finger is on both the second and third strings. Once you get this, it makes an amazing difference and it frees up your ring finger, and makes your chord changes faster. Remember, you're using the tips of your fingers and not barring. If you try to bar an A chord the first string will most likely be muted. I know I went against many of instructors and teachers that do not permit this, but I say we have to try different things to find what works best for us as individuals.
Give it a try and I hope I didn't confuse you.