Re-dyeing Hair?

I don't find that bleach, when properly applied to strong, healthy hair to be damaging. I don't think Jean Harlow or Marilyn Monroe did either. Do know that bleaching leaves the hair more porous and with less tensile strength. It should be treated more gently. Conditioners may be required to keep the hair looking its best and special shampoos may be needed to prevent stripping of the delicate toners usually applied to pre bleached hair.

I do hope when you say you 'dyed' your bleached hair, that you used a toner made especially for pre bleached hair. If you did, in fact, apply a regular, permanent color to your pre bleached hair, you are asking for trouble by coloring it, again. The darker the color you applied, the more trouble you can expect. You should know that recoloring bleached and 'dyed' hair does not remove the 'dye' you first used. What you would be doing amounts to adding color on top of color...

and the results are likely to be a strange and too dark color.

If you properly bleached and toned your hair, it could be safely recolored to approximate the color you had before bleaching. The use of special fillers may be required as a prerequisite. Do you even know what a 'filler' is? The procedure would require the expertise of a professional colorist, lest you end up with very damaged hair. The fact that you ask if it would be good for you to 'dye' your hair again is clear evidence you do not have the knowledge required for what you are attempting.

I've nothing against people coloring their own hair, but in this case, unless you are willing to seek out and pay for professional services, you are likely to be much more dissatisfied with a third color, than you were with your original color or the color you had after bleaching and 'dyeing' your hair.

Bleach and dye are incredibly damaging, Brandi. Why not try living with the results for a few months until new growth is long enough to style?

Treating your hair again before then will very probably result in severe damage and breakage. Your other option would be to buy a wig.