I have been searching for this as well but I am not aware of such an bicycle app. Might have overlooked something - glad if someone gives a good pointer!
Map and bike routing could be done with OsmAnd (on fdroid too).
OsmAnd is pretty flexible (you probably know, just stating: the data it operates on is free/libre, can be used offline, its routing cost functions can be changed, the underlying routing engine can be changed (e.g. to BRouter “Let’s get serious about bike routing”) and it has an API other apps can connect to)
Maybe also RunnerUp is an application to watch. I haven’t used it myself but it seems to have lots of things in place.
There might be two drawbacks though: a) it’s for runners;) b) it’s been excluded from fdroid builds because it uses ANT+ libraries (not compatible with free/libre and RunnerUp currently cannot be compiled without).
Eventually look for speed and cadence sensors which support both ANT+ and bluetooth. This helps if you ever plan to see your data both on the smartphone and a dedicated bicycle computer.
Once you have your ride data colllected you might be interested in the excellent GoldenCheetah (PC software, GPL v3, Linux, Mac OS X, Windows) for post ride analysis.