adjective

reserved, modest, and shy (typically used of a woman).

a demure young lady

modest,unassuming,meek,mild,reserved,retiring,quiet,shy,bashful,diffident,reticent,timid,timorous,shrinking,coy,decorous,decent,seemly,ladylike,respectable,proper,virtuous,pure,innocent,maidenly,virginal,chaste,sober,sedate,staid,prim,prim and proper,priggish,prissy,prudish,goody-goody,strait-laced,puritanical,old-maidish,straight,starchy,uptight,square,retired