he was the eldest son of nicholas bagenal and eleanor griffith, daughter of sir edward griffith of penrhyn. his brother was dudley bagenal. bagenal probably matriculated from jesus college, oxford when he was 16 (in 1572 or 1573), but left without taking a degree in order to join his father sir nicholas who was then marshal of the army in ireland. in may 1577, sir nicholas was appointed chief commissioner of ulster, with henry as his assistant. bagenal was himself knighted in 1578. he was involved in some military disasters, such as a defeat at glenmalure on 25 august 1580 when lord grey led the troops (with bagenal one of the commanders of the rear) into battle with fiach mchugh o'byrne and viscount baltinglass in the wicklow mountain passes. in 1584, bagenal was colonel of the garrison at carrickfergus when 1,300 of sorley boy macdonnell's scots landed on rathlin island. bagenal attacked but was ambushed at glenarm and had to retreat.