Exactly what Scriptor said. The stem of "bone" is oss, that of "mouth" is os.
The nominative ending in the third declension is usually -s, so oss-s -> *osss -> os, since Latin words never end in double s.
oss-s -> os
oss-is
oss-i
oss-s -> os
oss-e
oss-a
oss-(i)-um (the ambiguity here arises from the fact that the nominative theoretically ends in -ss, satisfying the rules for i-stem nouns, though technically, since os is neuter, its being i-stem based on its nominative's ending in a double consonant is irregular anyways. The form ossum is more regular, derived from the actual nominative os.
oss-ibus
oss-a
oss-ibus
Os as in mouth has the stem os, which also receives and loses the -s: os-s -> *oss -> os.
The other forms have a single s in between two vowels, which is bad news in classical languages. In Latin, it means the switch to r; for example: os-is -> *osis -> oris
os-s -> os
os-is -> *osis -> oris
os-i -> *osi -> ori
os-s -> os
os-e -> *ose -> ore
os-a -> *osa -> ora
os-um -> *osum -> orum (note that here there is no chance of an i-stem ending)
os-ibus -> *osibus -> oribus
os-a -> *osa -> ora
os-ibus -> *osibus -> oribus