Visa issues meant Bashir racked up 10,000 unwanted air miles shuttling between Abu Dhabi, London and Hyderabad, where he arrived just in time to take in the final day of England's win.
The 20-year-old has taken 10 first-class wickets in six games at an average of 67, while Leach's absence means England's three specialist spinners have three caps between them - two for Rehan Ahmed, one for Tom Hartley.
England captain Ben Stokes first floated the possibility of Bashir featuring on the tour of India six months ago after watching a video montage of him bowling to Sir Alastair Cook on his first Somerset appearance.
"To be perfectly honest, our training camp in Abu Dhabi was the first real live look I got at Bash," Stokes admitted.
"The first time I saw him was on Twitter. I think the County Championship put a little clip together of him bowling against Sir Alastair.
"I just saw something. With the height he bowled from, it was very obvious that he put a lot of action, a lot of revolutions, on the ball."
England men’s team to play India in 2nd Test
1. Zak Crawley
2. Ben Duckett
3. Ollie Pope
4. Joe Root
5. Jonny Bairstow
6. Ben Stokes (C)
7. Ben Foakes
8. Rehan Ahmed
9. Tom Hartley
10. Shoaib Bashir
11. James Anderson