I built my own bike hoist, really not that complicated with rope and pulleys. I used rope loops around the bike and carabiners as a disconnect between hoist and loops. Mountaineering carabiners will be weight rated if you *really* need it. I used pretty minimal carabiners, not even 1/4" rod sized.

You really do not have to overdo it here. If the bike really does weigh 100 lbs that is only 50 lbs on two lift points. The loading divides and reduces quickly. Nonetheless mounting to ceiling studs is mandatory and probably the one spot to over compensate with doubled up lag bolts/eyes (no shear working for you here, only pulling).

With that much weight you will likely want some kind of compound hoist though. The upside is reduction of force needed to lift the bike (and this can be huge) and the downside is you pull lots of rope. With my hoist I had compound action and it was still helpful to lift the bike while pulling the rope rather than just pull the rope.

Rope is plenty adequate for this job, there is really no need of steel cable. The only advantage of cable is that it will stretch less but it will be much tougher to manage the ends and tie off.