In standard Englishes, the vowel qualities of the SCHWA and NURSE vowels, /ə/ and /ɜ:/ respectively, are virtually identical as shown on this vowel diagram:
However, although these vowels are very similar in quality they are different phonemes. The NURSE vowel that we find in the word bird nearly always occurs in stressed syllables. SCHWA, on the other hand occurs exclusively in unstressed syllables. It will usually be much shorter in duration than an occurrence of the NURSE vowel.
If you tried to pronounce wonderful with a sustained second syllable, for example if you made the second syllable two or three seconds long, you would find the vowel to be indistinguishable from the vowel in bird.