What "bounces" is not dependent on mode like AM/FM etc. but on frequency and conditions that are favorable to those frequencies at any given time. AM broadcast frequencies are at the right place for bounce at night but they would still bounce if they were FM at the same frequencies. However because of Doppler shift, they won't sound too good.
FM transmissions at 50Mhz and even higher have been known to "skip" if conditions are right. Many hams have communicated across the pond on 50Mhz during the right conditions.
As for line of sight, VHF and above is generally that way. HF will "ground wave" and "skip" but since the skip is variable and unreliable, all military communications using HF were rated for ground wave distances. I often work several hundred miles on ground wave.
Today, almost everything military, other then the tactical radios, are satellite. The days of the ratt rigs passed after the first golf war.