Permanent hair dye which is well maintained is not usually considered a chatzitzah, a barrier to immersion in the mikveh. It is important that the coloring is still in good condition, and that the roots have not grown out enough that you would want to touch it up if you had an important event to attend. See our article on chatzitzah for a more detailed explanation.
If you are growing it out for good, and are truly not particular (you would be willing to attend a wedding in the current condition for example) in the intermediate stages, then it would also be ok. If you are particular about your appearance during this stage, then it would be preferable to use a temporary dye before going to mikveh so that your hair is all one color when you immerse.