Is the connection feasible? If you check the station map you can see it should be, there are only four platforms divided by trains and there's a subway (that's just a tunnel, it's just called a subway, to me a subway would be like an underground train but no, this is not a metro) between them. The signs are obvious and hard to miss. Everyone will flow there which also helps.
The reason I emphasized it should but it might not be right now because work is ongoing and the Bath-Bristol Temple Meads train was replaced by a coach just this weekend: https://www.gwr.com/travel-updates/planned-engineering/bristol2019 If that happens, being on time is extremely unlikely especially because there are roadworks on A36... The same is scheduled for Sundays 23 June and 7 July. If your travel is a weekend, tweeting https://twitter.com/gwrhelp or calling +44-345-7000-125 to confirm there is a train and not a coach is strongly advised. GWR doesn't do this workdays, that'd be madness.
Also note GWR sets a trap by putting garbage collectors as you leave the train but don't fall for it, hold on to your tickets until you exit the station. Despite they are checked on the train, they are also checked at the exit and you will be forced to buy a second ticket. On the other hand, CrossCountry is a very helpful company, I only had positive experiences with them.