AFAIK mainly two factors:

1) his standing in the family (faction heirs & leaders have additional bodyguards)

2) his personal security. the higher the bonus, the more bodyguards he gets.
the exact formula differs with the chosen unit size, but if I recall correctly should be 1:1 in vanilla on normal size.
note that a negative PS value decreases the number of bodyguards; this only comes into effect when the unit has lost men and thereafter regenerates to the new (lower) number.