Traditionally the correct expression is

"Hand loom woven bag"

However, with the many sites around that are not very well written, there are some strange variations on Google.

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Note added at 6 hrs (2016-08-23 18:38:20 GMT)
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You would also probably be correct to use "handloom" as one word.

"Handloom weaving is an art practised in the Philippines over generations. Up until the last century, it was a household activity to meet family needs and was not organised as a commercial industry."
http://www.bococo.co.uk/inspiration/blog/hand-loom-weaving/

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Note added at 6 hrs (2016-08-23 18:40:10 GMT)
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"The handloom was devised about 2,000 years ago and was brought to England by the Romans. The process consisted of interlacing one set of threads of yarn (the warp) with another (the weft). The warp threads are stretched lengthwise in the weaving loom. The weft, the cross-threads, are woven into the warp to make the cloth."
http://spartacus-educational.com/TEXweaving.htm

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Note added at 19 hrs (2016-08-24 07:49:50 GMT)
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Your choice: "Hand loom" or "Handloom".

I would say that older people, and traditionally educated users of English would definitely group these words together (handloom). But most of today's internet users would accept either version, and not see "hand loom" as incorrect.
---Unless you would prefer to try and compromise and use a hyphen (hand-loom), which would be debatable perhaps among language "Scholars/erudites/academics". ---
But at the end of the day, this is probably not worth arguing over.

Personally i would go for "handloom woven"!!