I’ve just been reading a selection of these, some in the first person and some in the third. I think I prefer the first, though there may be marketing reasons I don’t know about to go for the third.
The third seems a little stiff and formal to me, reminiscent of the way people used to speak to customers in stores: ‘Would madam care to consider our latest range of camisoles, straight from our suppliers in Liège?’
It seems particularly strange if you know, or have reason to believe, that the bio wasn’t written by a third party at all but by the author him or herself.
But I appreciate that an author’s bio written in the third person may give an impression of objectivity and so be deemed more reliable.