'retiringly' is formed from the adjective 'retiring', which comes from the verb 'retire' (from Old French 'retirer' meaning 'to withdraw, draw back'; 're-' meaning 'back' + 'tirer' meaning 'to pull/draw').

'retirer' (Old French) > 'retire' (Middle English) meaning 'to withdraw' > adjective 'retiring' meaning 'withdrawn, modest' > adverb 'retiringly'.

Initially associated with 'withdrawing' or 'drawing back', the word evolved to describe a person's modest or reserved (shy) manner; now it means 'in a reserved/shy manner'.