You may use your ticket, at no extra cost, on South Western Railway service between Weymouth and Southampton Central, where you can change for services towards Westbury and Bristol Temple Meads. This may extend your journey time by approximately 1 hour 30 minutes.
Had you been at Weymouth, waiting for the 17:28 to Bristol, you would have had the fortune to catch the 17:15 to Waterloo, which actually departed at 17:35. This is what would have then happened:
Arrive at Southampton at 19:17 (20 late).
Find you have missed the connecting Cardiff train due to depart at 19:11. Actually, you haven't missed it as it's been cancelled.
You find that the next Cardiff train, the 20:11, has also been cancelled.
There's a 19:37 to Salisbury, so you catch that. It departs 5 late.
Arrival at Salisbury is at 20:22 (7 late).
There was actually a Salisbury-Bristol train running (most were cancelled today as part of service-thinning)...
It left on time at 20:11, so you have missed it. Bad luck!
Next train should be the 20:42 Cardiff... but it's cancelled.
Also cancelled is th 21:42 Cardiff train...
So you catch the 22:11 Salisbury-Bristol train, due into Temple Meads at 23:32. (Instead of 20:12 when the Wey-Bristol was due)
Train services running to and from these stations have been suspended. Disruption is expected until the end of the day.
I would take "suspended" as meaning complete cessation of trains.
But the 20:14 departure from Weymouth ran, arriving Bristol at 22:45.
Mind, it was a 2-coach class 165, so would have been rather cosy if everyone waited for it.
The final train, the 21:28 Weymouth-Westbury was also cancelled.