Bowen is usually a Welsh name, from Pembrokeshire. It means "Son of Owen".
I suppose it could seem more Chinese if spelled differently: Bo Wen, or Bo Hwen (but 'Bo' does not seem Chinese to me).
There are at least seven ways of writing Chinese in the Roman alphabet, none of them very logical to English speakers. Westerners devised the Wade-Giles system and the Yale systems, the Postal system (used for place names) and EFEO (devised by the French). The Chinese devised the Qien Xinzi (for the Min language) and Bopomofo systems. Hanyu Pinyin seems to be the favorite these days, because the government of the PRC has adopted it.
It is not obvious how to pronounce Chinese to most English speakers. Mao Tse-Tung and MaoZedong are two spellings of the same name, as are Zou Enlai and Chao En-Lai. It certainly is not obvious to any English speaker how to pronounce Qien Xinzi.
Part of the problem is that there is no logical way to express tones in the Latin alphabet, and Chinese languages have several tones (four is the usual number, I think). Those funny marks used in spelling Vietnamese are a Frencophine attempt to transcribe tones: as I do not know Vietnamese, I cannot comment on how effective or accurate this really is. But it does seem to work for the Vietnamese, at least.
And then there are various different Chinese languages: among them Mandarin, Cantonese, Min, Wu, plus a variety of languages (sometimes inaccurately called 'dialects' ) of minorities that are not Han Chinese.
The International Phonetic alphabet would be most accurate, but it is rather complicated.