Help me identify this Sci-Fi book please?

Hi all, and thanks in advance for reading my sketchy ramblings. I've asked this about a year ago, thought I'd ask again.

Like most of these half-remembered plot lines I'm not exactly sure that my memory stands up particularly well, but here goes.

Set in some post-apocalyptic era the male lead character finds an ancient automated library and meets the female lead character about the same time. Finding some way to ask the library questions about the disappearance of the population, the library provides the woman with a book that instructs her how to develop mental abilities but the man's not convinced. She sticks with it and demonstrates that it works (and some specific thing about a flower used by her to show her abilities). He starts learning and catches up and they learn to (transport|jaunt) themselves. More information about the population having left the planet in this way and pointers to their destination. Leap of faith into the unknown taking a bubble of air with them and getting low when, at a final push, meet some that have already travelled. Further demonstration of how mental abilities can be further developed and a meeting held for reasons of privacy in a mind-bubble in the heart of a star.

I have no idea why this popped into my head but I'd love to track it down again. Any pointers gratefully received.

'Jaunt' appears in a lot of written Sci Fi - 'The Stars My Destination' in 1956 well before the 'Tomorrow People' and Steven King's 'The Jaunt' as examples. Absolutely not H G Wells's 'The Time Machine'. Not a Star Trek original series episode 'All Our Yesterdays' with Mr Atoz's library.