It didn’t have much to do with bribes and threats. Janos Slynt was Commander of the Iron Gate, and was promoted when his highborn commander, Manly Stokeworth of House Stokeworth, died. It’s likely that this happened right after the Sack of King’s Landing, where a lot of the nobles who would normally hold posts in the Gold Cloaks were invalidated by their support from the Targaryens, so Jon Arryn promoted from within.