In Latin, there was total regressive assimilation in a combination of an occlusive (Verschlusslaut) followed by f:
OCC+f> -ff-
Examples:
affero < *at-fero < *ad-fero (recomposition also possible - adfero)
offero < *op-fero (recomposition also possible - obfero)
effero < ec-fero (recomposition also possible - ecfero)
cf. Weiss 2009/2011: 172, "Latin does not normally have f in non-initial positions. The few examples are in compounds and the family of inferus."
Also note that the group "bt" in Latin was most likely pronounced [pt] (Tronskii 1960: 114). Prefixes ab-, ob-, and sub- are usually reconstructed as PIt. *ap-, *op-, and *sup- (Tronskii 1960: 113, de Vaan 2008).
As for aufero (and aufugio), here's what you can find in de Vaan 2008:

In a combination of a labial/velar followed by s+C, the first consonant (labial or velar) was lost:
ostendo < *ops-tendo
suscipio < *sups-capio
suspicio < *sub-specio etc.
cf. Leumann 1977 "Neben ab ob sub stehen die mit s erweiterten Formen abs- obs- subs- bzw. aps- ops- sups-, fast nur als Praeverbien [...] Die s-Formen stehen nur vor Tenues, besonders in altertuemlichen Komposita; oefters sind sie vereinfacht zu os- sus-, vor p auch as- [...]" (p. 157).
Ernout & Meillet 1985/2001, "ce dernier [obs-; Alex B.] usité seulement en composition; [..] il est souvent réduit à os-" (p. 454).
So, as you can see (Ernout & Meillet 1985/2001, Leumann 1997), the form obs- was usually used in compounds.
References:
Ernout, Alfred, Antoine Meillet, and Jacques André. 2001. Dictionnaire étymologique de la langue latine: Histoire des mots. Paris: Klincksieck.
Leumann 1977, § 203. - Leumann, Manu, J. B. Hofmann, Anton Szantyr, and Friedrich Stolz. 1977. Lateinische Grammatik: Lateinische Laut- und Formenlehre. München: Beck.
Pfister 1977, §137.2. - Pfister, Raimund. 1977. Handbuch der lateinischen Laut- und Formenlehre. Band 1, Einleitung und Lautlehre. Heidelberg: Winter.
Tronskii 1960, §232, 268. - Tronskiĭ, I. M. 1960. Istoricheskai︠a︡ grammatika latinskogo i︠a︡zyka. Moskva: Izd-vo lit-ry na inostrannykh i︠a︡zykakh.
Vaan, Michiel Arnoud Cor de. 2008. Etymological dictionary of Latin and the other Italic languages. Leiden: Brill.
Weiss, Michael L. 2011. Outline of the historical and comparative grammar of Latin. Ann Arbor: Beech Stave Press.