drtracer is right, it was not fuel injected, no production Bridgestone was ever fuel injected as far as I know, they all had carbs.
If you go to this page you can download a sales brochure from 1966:http://bridgestonemotorcycleparts.com/index.php?action=downloads;sa=view;down=43
If you look at the brochure you will see they only mention OIL injection on the 175, but not on any of the smaller models. I would guess that since your Dad said he had to mix oil with the gas that his 90 did not have OIL injection either.
So... I would say that you Dad's bike was neither fuel injected or oil injected. Not that it really matters, it is still a cool little bike.