Bay Tree Not Growing

I have a bay plant that is 2 years old. I have it in a 5 inch pot in partial sun. It seams like it has stopped growing, although it is still green. My question is: should I transfer it to a larger container or can I plant it in the yard? Can I transplant it now or should I wait until spring? If I plant it in the yard do I need to protect it from cold? I live in south Louisiana near the Gulf Coast.

We find that bay trees will have a growth spurt in spring and summer, but by late summer growth slows or stops altogether. There is nothing wrong; it is the normal annual cycle for this plant.
Repotting into a larger pot is unlikely to induce new growth. If the plant is potbound, you will need to move it up to a larger pot sometime before the next growth spurt.
Bay is hardy in your area. Bay tolerates a few degrees a frost in winter. You could plant out now. Make sure that the soil is well drained because it does not tolerate excess water in the root zone.