I have recently been employed in Bangkok, I have got my non-immigrant Bvisa from my native country (for 3 months), and I would be getting my work permit in a weeks time (after which I start my work legally).

If I understand right, my WP will be valid till the date of my Non-Immi B Visa. And after I extend my visa, my WP can be updated to the date of my visa expiry (new).

Now my question is how can I extend my non-immigrant visa for 1 year when my 3 month non-immi B visa is about to expire??

Previously I was in Thailand on a Non-Immi 'F' Visa and as such I could just extend my visa yearly

Looking forward to some suggestions...

Now my question is how can I extend my non-immigrant visa for 1 year when my 3 month non-immi B visa is about to expire??

Talk to your employer - you'll need his cooperation, extensively. On his side there's a lot of requirements that he must be fulfill. Have a look at Case 7.1 in this document: http://www.immigration.go.th/nov2004/2notice/rtp606EN.pdf - That's the official (translated) list of requirement for each kind of one-year extensions - 7.1 covers regular employment.