Kammala wannan jumla: Bayan kammala karatunsa daga Fairfield College Preparatory School, Quebec Nordiques sun zaba Drury a matsayin na 72 a zagaye na uku na gasar cin kofin duniya na shekara ta 2000
1994 NHL shigarwa daftarin. Bayan an tattara shi, ya fara aiki na shekaru hudu a Jami'ar Boston (BU). A shekararsa ta farko a 1995, ya lashe gasar zakarun kasa tare da BU. A duka 1997 da 1998 an kira shi dan wasan Hockey East na shekara kuma an kuma kira shi mafi kyawun mai karewa a shekarar 1998. A cikin shekararsa ta ƙarshe, ya sami lambar yabo ta Hobey Baker a matsayin babban dan wasan wasan hockey na kankara na National Collegiate Athletics Association (NCAA) bayan ya zama na biyu a kakar da ta gabata. Drury shine dan wasan BU na farko da ya kai burin 100 da taimakawa, ya gama da 113 da 100, bi da bi. BU ta lashe gasar Beanpot duk shekaru hudu da ya buga mata. A ranar 15 ga Janairu, 2009, a cikin aikinsa na NHL, an kira Drury Hockey East's Best Defensive Forward, a matsayin wani ɓangare na bikin cika shekaru 25 na gasar. An zabi Drury a cikin kuri'un magoya bayan Hockey East da membobin kwamitin bikin cika shekaru 25 na gasar.