The links above for the bus timetables at Trebes no longer works so here are the updated ones
Number 10 local bus
The bus journey takes about 20 minutes. There are no buses in the evenings nor all day Sundays and holidays.
The only journey on route 948 leaves Carcassonne at 0649am, long before the first bus from Trebes arrives.
The train journey from Carcassonne to Toulouse takes between 45 minutes and 1 hour depending which train is taken. Trains are irregular and at weekends rather infrequent.
This will not be much different in summer but do check locally.