Bio

[Nonverbis]

https://www.oxfordlearnersdictionaries.com/definition/english/bio?q=bio
https://dictionary.cambridge.org/dictionary/english-russian/bio
https://www.macmillandictionary.com/dictionary/british/bio

/baɪəʊ/

Could you tell me how many syllables are there in this case?

Please, pay attention to the fact that the stress has not been signified in any of these dictionaries.

So, what we have here:
1. The absense of a stress implies one syllable. Or we will have to trust in a theory of a plot not to put a stress here. The publishers of these dictionaries are independent. Or they just copy-pasted this pronunciation, which I hope not the case.
2. We remember that in English there can be only one vowel in a syllable.

Therefore there is one syllable here.

But in this cae it is longer than a triphthong. It looks like a tetraphtong, which is unknown to linguistics.

Could you comment on this?

 

[jutfrank]

Two syllables. The stress is on the first. Both syllables include a diphthong.

 

[Nonverbis]

But why don't they signify the stress?

 

[5jj]

Possibly because the compilers of the dictionary consider it only a part of a longer word. If you look up such words, for example, biodegradable, the stress will be marked.

 

[Skrej]

In English, every time you have a separate vowel sound, you have a new syllable. Note that I said 'vowel sound', not written vowel. Since you hear two distinct vowel sounds in 'bio', it has two syllables.

Now that I think about it, that's probably true of many or maybe even most languages, not just English.

 

[jutfrank]

But why don't they signify the stress?

I think it's because in prefixation it isn't always stressed on the first syllable. Think: biologist and bionic.