The success came after a tough few years for the flame-haired Yorkshireman, who was dropped for the 2013-14 Ashes tour and has come under criticism for his keeping behind the wickets.
"You go back maybe two years and there are people writing you off to never play test cricket again," Bairstow told Sky Sports after surpassing the 1,045 run-haul accumulated by Zimbabwe's Andy Flower in 2000.
"To then come back and prove a few people wrong with the way that I've been playing ... there were a few mumbles floating around that I wasn't good enough."
Despite having Michael Vaughan's 14-year-old England record for the most test runs in a calendar year (1,481) within his sights, Bairstow is not taking anything for granted.
"There's still a lot of cricket to play this year and hopefully I can carry on in the same vein with the bat and the gloves," he said.
"Having missed out for 18 months after the Ashes and going away and working on my game and playing for Yorkshire and earning your place back, you want to play as many games as you can for England in every single format going."
England face Bangladesh in the second test in Dhaka starting on Friday.
(Reporting by Nivedita Shankar in Bengaluru, editing by Nick Mulvenney)
