Train from Bristol to London

You can just show up and buy the ticket on the day but advance tickets work out cheaper but are non refundable and for specific train only. Check out GWR.com
Note that Temple Meads is the downtown station and that Parkway is north of the city mainly served by trains going between London (PAD) & south Wales.

There is a type of ticket called Advance. They are limited in number and when they sell out at the cheapest price point, another limited number go on sale at a slightly higher price point. Then, once they sell out the next tranche goes on sale, and so on. This type of ticket is only valid for the specified train

Other ticket types are Anytime (fully flexible and Off Peak (semi-flexible) - they are fixed price - never sell out and are the same price whether you buy six months ahead or on the day at the station.

So, understand the difference between buying a ticket in advance and an Advance ticket.

https://www.seat61.com/train-travel-in-britain.htm#guide-to-train-fares

The simpler and more direct answer is that if you travel on a weekday before 9 am you will pay £105, between 9am and 10am £58, after 10am £41, on the day at the station. £41 all day Saturday and Sunday.

If you book reasonably far in advance off peak (after 9am) train specific fares are available starting at £25. Even 2 days ahead you will get a fare for £35.
Book say a fortnight ahead and you will even get a peak train for £47.

Unless you are absolutely scrimping you don't need to book anything like 12 weeks ahead, which is the oft quoted advice.

Use the actual train operator's website, in this case Great Western, if you can. I don't know why the Man in Seat 61 tries to direct you to Transport for Wales website.

I know you have asked about trains. But for the sake of completeness National Express, Megabus and Flixbus also run services to London, which take 3 hours or less. National Express run better than hourly from 4.15am and advance fares start from just £3.50.
The Coach Station is right in the City Centre, Temple Meads station is on the fringe of the city. The fun way from the City Centre is on the waterbus. https://www.bristolferry.com/waterbus/

Booking well ahead was good advice when there were really dirt cheap Advance tickets available in small quantities. Today this is not so much the case on many routes. The rock bottom fare is £20 outside of promotions (not considering the indirect route via Salisbury). Do look out for promotions on the GWR website - you can join their email list if you want.

Thank you for all of this valuable information.