This question reminded me of a Nanowrimo attempt of mine a few years ago.
Main Character is bicycling in modern day (2013 at the time), and creates a time-portal, finds herself in 1963 near Xavier's School for the Gifted. She's genre-savvy, realizes she's probably a mutant, so goes there. She's a self-insert, so lacks combat skills, and is killed quickly to make another character (probably Angel grow emotionally.
But the Bike is left behind. Not an enchanted motorcycle, not even a super fancy racing one, just something perfectly normal (though slightly higher-end to be lighter) for commutes in a small town, and a helmet. And of course bikes have existed for almost a century before the X-Men (1886 = bikes looking pretty modern), so the concept isn't new.
But materials from 50 years in the future? Wikipedia states:
Historically, materials used in bicycles have followed a similar pattern as in aircraft, the goal being high strength and low weight.
So perhaps her bike was a Titanium Alloy? In other words, biomedical-standard materials or aeroengineering materials appearing first via the bike, not the other way around?
Other things that I figure she would have (and bring back in time)
- LED flashlight (1960s LEDs could only function in red frequencies -- it took until the 1990s for "white" LEDs to exist;
- a helmet (pre-1970s they were mostly leather, modern ones have polystyrene, polycarbonate, new manufacturing methods for that microshell with forming things
- Under-Armour type performance wear (synthetic fabrics of course existed back then, but I'm sure 2010s ones are different
The Question: How much would technology change if such materials from 2013 were available in 1963?
Feel free to ignore the Professor X & Mutants angle.... the main point is 2013 --> 1963. The modern person (who doesn't especially know materials science) is gone, so she can't explain things, but there are intelligent people around to examine and understand the materials to the best of their 1960s abilities.