Tinkler, who missed June's European Championships to focus on her school exams, was part of the bronze medal-winning British team at the 2015 World Artistic Gymnastics Championships in Glasgow.
She will get her GCSE results the day after returning from Rio, saying: "I've got that look forward to now."
Beth Tweddle, London 2012 bronze medallist and BBC Sport analyst:
"It is amazing. The British team have worked so hard to get here.
"All credit to Amy for performing under such pressure. To take that bronze medal, it is incredible."
Biles' gold capped a stunning Olympic debut for the teenager, who was too young to qualify for London 2012.
She becomes only the fifth woman to win four gold medals at a single Games, after Agnes Keleti and Larisa Latynina for Hungary and the Soviet Union respectively in 1956, Vera Caslavska for Czechoslovakia in 1968 and Romania's Ekaterina Szabo in 1984.
"It's very crazy. To think what I've done," said Biles. "It's been an amazing experience and I don't think I could be more proud of myself.
"Your first Olympics you walk away with five medals, that's not tough at all. Especially four being gold, that's just unheard of. I'm very proud."
Inspired to try gymnastics?
Since starting her senior career in 2013, the 19-year-old is undefeated in all-around competitions.
Biles, from Texas, became the first black gymnast to win the all-around title at the World Championships in 2013 and, after retaining her crown in 2014, she won an unprecedented third successive all-around gold in Glasgow in 2015.
She has 10 world golds to her name, more than any other woman in history - and 14 medals in total.
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