'archegonial-bearing' is a compound formed in Modern English from 'archegonial' + 'bearing'. 'Archegonial' derives from New Latin 'archegonium' (from Greek 'arkhē-' meaning 'beginning, principal' + Greek 'gonē' meaning 'offspring, seed, generation'), and 'bearing' comes from Old English 'beran' meaning 'to carry, to bear'.

'Archegonium' entered scientific New Latin from Greek arkhegonion; it was adopted into botanical English as 'archegonium' and then adjectivized to 'archegonial'. In Modern English botanical usage the adjective was combined with the English present participle 'bearing' to form the compound 'archegonial-bearing'.

Originally the Greek-based element referred to an organ related to origin or generation; in botanical New Latin it came to denote the specific female gametangium 'archegonium'. Over time, compounds like 'archegonial-bearing' have come to mean simply 'having/producing archegonia' in technical botanical contexts.