Bullen has pulled his Achilles tendon and Paul Sturrock admits he is touch and go for the clash with Wolves tomorrow and one of the Dundee clubs on Sunday in the Discovery Cup.
The skipper played in every-single game last season bar the FA Cup defeat at Swindon and he was tipped to play in attack.
Wood meanwhile has broken his nose and missed the Partick Thistle draw on Wednesday.
Graham Coughlan should start in defence with Patrick Collins for the friendly tournament in Scotland.
The Owls' other injury victims are Drew Talbot, Drissa Diallo and JP McGovern.