Pedzisa mutsara unotevera: Mushure mokunge apedza kudzidza paFairfield College Preparatory School, Drury akasarudzwa neQuebec Nordiques 72nd yakazara mumutambo wechitatu we
1994 NHL Entry Draft. Paakasarudzwa, akatanga basa remakore mana paBoston University (BU). Mugore rake rokutanga muna 1995, akahwina mukombe wenyika neBU. Muna zvose zviri zviviri 1997 na1998 akatumidzwa zita rekuti Hockey East mutambi wegore uye akatumidzwawo zita rekuti akanakisa kudzivirira kumberi muna 1998. Mugore rake rekupedzisira, akahwina mubairo weHobey Baker semutambi wepamusoro weNational Collegiate Athletics Association (NCAA) mushure mekupedza semumhanyi mwaka wapfuura. Drury aiva wokutanga BU mutambi kusvika 100 basa zvinangwa uye anobatsira, kupedza pamwe 113 uye 100, zvichienderana zvakadaro. BU yakakunda mutambo weBeanpot makore ose mana ayo akaitambira. Musi waJanuary 15, 2009, zvakanaka kupinda muNHL yake, Drury akatumidzwa zita rekuti Hockey East's Best Defensive Forward, sechikamu chekupemberera kwegore re25th. Drury akasarudzwa mukuvhota kwevateveri veHockey East nenhengo dzeKomiti yeLigi yeC25th Anniversary.