While bzero and bcopy functions aren’t ISO C (the actual standard that I assume you’re talking about when referring to them as non-standard), they were a POSIX standard thing, although they pre-dated both ISO and POSIX.
And note that use of the word “were” – these functions were deprecated in POSIX.1-2001 and fianally removed in POSIX.1-2008, in deference to memset, memcpy and memmove. So you’re better off using the standard C functions where possible.
If you have a lot of code that uses them and you don’t want to have to go and change it all (though you probably should at some point), you can use the following quick substitutions:
// void bzero(void *s, size_t n);
#define bzero(s, n) memset((s), 0, (n))
// void bcopy(const void *s1, void *s2, size_t n);
#define bcopy(s1, s2, n) memmove((s2), (s1), (n))