I have used maps.me until a few years ago but was never really happy with the performance of the bike routing algorithm.
I've switched to Osmand [1] and BRouter [2] (both available on F-Droid) and nerver looked back. BRouter on Android is a bit tricky to set up (you need to download routing tiles in addition to the map files through a really ugly UI), but once you're done it's the best bike navigator I can think of (and it's really fast).
The BRouter profiles are highly customizable, check out Poutnik's repositories [3] for examples. Some of his profiles and many others con be tested on https://brouter.m11n.de/ (german).