C standard libraries on bare metal
Yes, there is a standard, simply the C standard library. The library functions do not require a "full blown" OS, or any OS at all, and there are a number of implementations out there tailored to "bare metal" code, Newlib
perhaps being the best known.

Taking Newlib as an example, it requires you to write a small subset of core functions, mainly how files and memory allocation is handled in your system. If you're using a common target platform, chances are that someone already did this job for you.

If you're using linux (probably also OSX and maybe even cygwin/msys?) and type man strlen, it should have a section called something like CONFORMING TO, which would tell you that the implementation conforms to a specific standard. This way you can figure out if something you've been using is a standard function or if it depends on a specific OS.