Sorry for Disturbing

Hello!

What Do [This is more polite] you think that I can I start an e-mail with the phrase:
"I am very sorry for disturbing [or "bothering"] you on during the holidays."?

I need to get some information from our Chinese supplier, but all the of China is on holiday now. but However, the person from that company my contact is still answering my e-mails.

Nothing wrong at all.  As a matter of fact, it is most appropriate for this context and circumstance.

    Hello Anna. How are you?

It is  generally  appropriate to be apologetic. It is a good message that you have.

sorry for disturbing

Hello!
What do you think, can I start an e-mail with phrase:
"I am very sorry for disturbing you on Holiday."?
I need to get some information from our Chinese supplier, but all the China is on holiday now, but the person from that company is still ANSWERING my e-mails.

sorry for disturbing

Hello!
What do you think, can I start an e-mail with this phrase:
"I am very sorry for disturbing you on Holiday."?
I need to get some information from our Chinese supplier, but all the China is on holiday now, but the person from that company is still answering my e-mails.

maybe instead "for disturbing" I would "to bother you"