That compares to 1h 10m by plane, so with check-in and getting to and from Bristol Airport and Edinburgh Airport (9 miles from Edinburgh) perhaps 4 hours?
Having done a similar journey (Stansted to Edinburgh) several times this year (once by train, three times by plane), I can confirm 4 hours is about right for the total travel time when flying, assuming about 45 minutes travelling time to the airport at the England end and a taxi to the city centre at the Scotland end. This also assumes you are not checking in any luggage and capable of getting through security without flustering around too much (i.e. read up what's not allowed before travelling so your luggage doesn't need to be searched by hand). Domestic arrivals at Edinburgh are dumped into the departure lounge, from where you can exit to the taxi ranks very quickly.
On the train journey, it took about 8 hours (total travel time, including connections either end) due to a delay. Nevertheless, flying offered the option of making a day return (therefore saving on hotel costs), that wouldn't have been possible by train, even without the delay.