Hi,
I am guessing this is a white t shirt or without white ink. If it is have you tried an RTP apparel shirt to see if this makes any difference. These are already pre treated and it would tell you if the ink is bleeding and soaking into the fibres. If it is bleeding you can also try a light pre-treatment to stop the ink from doing this or anhigher quality t shirt.
Hope this helps, just MHO.
Colin