Would this not be "I have my bag (on me)". To say I need my bag would it not be " Tá mo mhála ag teastáil uaim" or "Ba mhaith liom mo mhála" or "Táim iarriadh ar mo mhála"?
bí ó is also a way to express 'want', so this is 'I want my bag'. To me, ag teastáil uaim is more like 'needing' (in Conemara, teastaigh only means 'need'). Though Tá mé ag iarraidh mo mhála should be acceptable.