'everblooming' is a modern compound formed from the adverb 'ever' and the present participle 'blooming' (from 'bloom'), literally meaning 'always flowering'.

'ever' originates from Old English 'æfre' meaning 'always'; 'bloom' comes from Old English 'blōma' (flower, blossom) → Middle English 'blome'/'bloom', and the present participle 'blooming' was combined with 'ever' in modern English to create the compound 'everblooming'.

Initially the parts meant 'always' ('ever') and 'to flower' ('bloom'); combined in modern usage they produce the descriptive sense 'always in flower' or 'continuously flowering'.