I don’t often use bullhorn outside of combos, but this is what I do when I try to combo.
sHK (cc) - hold the HK button: wait a bit, cHP xx (release kick button) Bullhorn
sLP /sLK / sMP xx EX Bullhead xx VT (hold the HK button from activating VT), cHP xx (release HK Button) Bullhorn
In midscreen neutral, I only use Bullhorn if I’m feeling gutsy in punishing a shoto fireball. In that case I hold the LP button. If the opponent for a random reason dashes forward to catch me off-guard, then I still have my 4f kicks. Bullhorn might be his worst anti air, hitbox wise compared to fHK, cHP or cMP, so I never use it for that purpose.
In VT it gains a lot more active frames and gains 2f~3f of armor from around startup frame 2, but I haven’t tested it extensively. The opponent can usually block in time if you want to make use of the armor to anti air the opponent.