Hotel to Appian Way?

Any suggestions?

Looks like there is a bus- Line 118- that'll take a bit over an hour.
Or a mettro/bus combo.
I'm not familiar with buses in Rome though, never taken any!

Does Rick's Rome guide book have info on how to get there?

I would just have hotel call for a taxi- shouldn't take more than 15 min? maybe 20 euros at most?

Depends on your definition of "best". The most convenient would be to taxi or Uber door to door, though that will be the most expensive too.
When we did this years ago (walking not biking) we took the metro to a nearby stop where we hopped on a local bus that dropped us at the entrance to the visitor center, where they had bikes for rent and a pretty good map of the various routes. You'll have to research that option for yourself - I've long since forgotten the stops.
One note: the portion of the Old Appian Way that we walked was decidedly not bicycle friendly - the uneven spacing of the ancient stones plus modern erosion would have made for an extremely uncomfortable ride. Was later told that there's a nice, smooth stretch out near the aqueducts that was bike friendly but we didn't make it that far on foot. Might be worth researching that as a better option for cycling.

Thank you both!

We also took a bus and rented bikes at the visitor centre. We did find it bikeable but we are used to riding on mountain bike trails. It was a lovely day and we plan to do it again when we go to Rome next spring.