The National Rail site returns a rail routing of Elizabeth Line only one stop to Hayes & Harlington, then flipping directions on the Elizabeth Line and taking it to Reading, then picking up Great Western to Bristol from there. That is the cheapest rail option and almost exactly the same amount of time as going HEX-Padd-Bristol, and same amount of time as the bus. It also offers more flexibility because that train routing goes every half hour or so, and the buses run every hour, so you have less waiting time. The change of direction at H&H probably not fun with big luggage, but personally I would like this much more than a bus ride. If you add a few dollars and buy as an offpeak one way, you can get on any train on this route as long as its off peak timing.