Today (Friday 3rd March), 2401 is diagrammed the following service:
12:00 Weymouth
12:54-12:59 Bournemouth
13:13-13:14 Brockenhurst
13:28-13:30 Southampton Central
13:48 Winchester
14:20 Woking
14:49 London Waterloo
I'd guess it'd work the 15:35 return (16:00 Woking, 16:33 Winchester, 16:49-16:51 Southampton Central, 17:20 Bournemouth arriving at Weymouth 18:19). This return journey is not confirmed, just my guess!
12:00 Weymouth
12:54-12:59 Bournemouth
13:13-13:14 Brockenhurst
13:28-13:30 Southampton Central
13:48 Winchester
14:20 Woking
14:49 London Waterloo
I'd guess it'd work the 15:35 return (16:00 Woking, 16:33 Winchester, 16:49-16:51 Southampton Central, 17:20 Bournemouth arriving at Weymouth 18:19). This return journey is not confirmed, just my guess!