Absolutely I would go. Dry until 2pm, then a 32% chance of rain until 5pm, then 65% chance for a couple of hours.
Where I am today in the Lake District we are under a 2 day weather warning for rain, with a risk of transport and power disruption (yes, really). It should have been bucketing it down now for 5 hours.
So far all we have is the lightest of drizzle.
There's a one hour round trip river cruise at Bath (covered boats)- https://pulteneycruisers.com/
If it got really wet I might be inclined to hop back on a train or bus and go to the museums in Bristol, 15 minutes away by train, 1 hour by bus.
There is a City sightseeing open top HoHo bus in Bath. I don't know about Bath, but up here the open tops have a covered section at the front. I like doing the open tops on a wet day sat in the covered bit as the buses are normally empty. You still get the fresh air and the expansive views.