C'est vrai que c'est étonnant que phonétiquement ce soit pareil alors que... ça ne l'est pas vraiment
ˈmʌð.ər
http://dictionary.cambridge.org/dictionary/british/mother_1?q=mother
bʌs
http://dictionary.cambridge.org/dictionary/british/bus_1?q=bus
En 'phonétique du pauvre', dans bus, c'est plutôt "beuss" et dans mother, "mozeur" (avec un o assez fermé toutefois)
Sur les pages citées, on entend bien la différence (ça me rassure car je ne prononce par meuzeur...)
AJOUT: il suffit d'écouter pour se rendre compte que ce n'est pas exactement la même chose !!
Cf. extrait de Wikipedia sur ce phonème, qui montre bien que sa prononciation peut légèrement varier:
http://en.wikipedia.org/wiki/Open-mid_back_unrounded_vowel
Before World War II, the /ʌ/ of Received Pronunciation was phonetically close to a back vowel [ʌ]; this sound has since shifted forward towards [ɐ] (a near-open central vowel). Daniel Jones reports his speech (southern British), as having an advanced back vowel [ʌ̘] between his central /ə/ and back /ɔ/; however, he also reports that other southern speakers had a lower and even more advanced vowel approaching cardinal [a].[4] In American English varieties, e.g., the West and Midwest, and the urban South, the typical phonetic realization of the phoneme /ʌ/ is a central vowel that can be transcribed as [ɜ] (open-mid central).[5][6] Truly backed variants of /ʌ/ that are phonetically [ʌ] can occur in Inland Northern American English, Newfoundland English, Philadelphia English, some African-American Englishes, and (old-fashioned) white Southern English in coastal plain and Piedmont areas.[7][8] Despite this, the symbol ‹ʌ› is still commonly used to indicate this phoneme, even in the more common varieties with central variants [ɐ] or [ɜ]. This may be due to both tradition as well as the fact that some other dialects retain the older pronunciation.[9]