The 21-year-old France international was given the suspension a week ago for a shoulder charge that knocked out Salford scrum-half Theo Fages and he sat out last Friday's game against Warrington.
Bousquet admitted the offence when he appeared via Skype in front of the Rugby Football League's disciplinary committee but the Catalans contested the severity of the ban. The club risked having the ban increased but the RFL's appeal panel ruled on Tuesday the original punishment should stand.
The Dragons' disciplinary worries worsened when full-back Brent Webb was given a one-match ban after being found guilty of fighting.
The former Leeds player was sin-binned, along with Warrington's forward Ben Westwood, during his side's 24-16 defeat by the Wolves last Friday.
Webb will miss his side's game at Castleford on Sunday but stand-off Leon Pryce will be available after he admitted a grade A charge of kicking out in the tackle.
Pryce avoided a ban but forfeited his right to submit another early-guilty plea for 12 months.
Like Webb, Westwood was given a one-match ban, ruling him out of Warrington's trip to Hull on Saturday.