Unfortunately, once you start coloring it, you will either have to continue to color it forever (which will undoubtedly cause damage to your hair), or at some point in time, you will have to let the coloring grow out, which would be more noticable than what you have now. 

Is your hair already chemically treated for color?  If not, then you might consider cassia (what some people call neutral henna, or colorless henna).  That might add some shine and depth to your natural color.  If your hair is already colored, you would need to do a strand test to make sure the cassia doesn't turn your hair green or orange (which is a reaction to the metal that is used in a lot of hair dyes.)

Sorry I don't have any better solutions. 

I have very different hair color, but I know that some of my naturally blonde friends use sun-in and lemon juice on their roots that sometimes grow in slightly darker.
From personal experience I know that sun-in or lemon juice can be brutal on dark hair, but I've seen great results on lighter hair.
Also, maybe its just better to wait for the summer? Your hair might naturally lighten up.

Hi there, It is that your new regrowth is coming in a diffrent color than the rest of your hair, liike changing naturally?

The ashiness might be due to chemicals in your water. Although I would think all your hair would be green then. You can try either using a clarifying shamppo to remove the minerals or you can try these at home remedies:

APPLE CIDER BUILD UP REMOVER

Ingredients:
1 ounce apple cider vinegar
1 quart of distilled water.

Directions:
Combine the apple cider with the water, stir. Pour through hair to get rid of buildup and soften hair at the same time. Rinse with tap water.


You can also try honey. Honey is a natural peroxide and over time, can lighten the hair.

Wash and condition hair, leave towel dried. Take a 1/4 cup honey and 2 tbs of lemon juice. Using a large paint brush, on towel dried, damp hair, brush the mixture onto the drab 2 inch root area.  Cover with a clear shower cap, loosley. Leave on for at least an hour then rinse. Try this several times untill you see the drab go away.

Hope this helps  Good luck hun!

Yes, the honey is very moisturizing and Yes, the acidity of the lemon does lighten. Honey has a natural Hydrogen peroxide. It is also has an acidic pH level. Here is some info on honey via wikipedia:

Hydrogen peroxide
Hydrogen peroxide in honey is activated by dilution. However, unlike medical hydrogen peroxide, commonly 3% by volume, it is present in a concentration of only 1 mmol/l in honey. Iron in honey oxidizes the oxygen free radicals released by the hydrogen peroxide.

C6H12O6 + H2O + O2 → C6H12O7 + H2O2
When used topically (as, for example, a wound dressing), hydrogen peroxide is produced by dilution with body fluids. As a result, hydrogen peroxide is released slowly and acts as an antiseptic.

Acidity
The pH of honey is commonly between 3.2 and 4.5.[41] This relatively acidic pH level prevents the growth of many bacteria.