I've never dyed my hair before. Please answer these questions.

-Should I use permanent hair dye after bleaching my hair?

Not really. And permanent dyes, especially on bleached hair, never last as long because the peroxide in the damages your hair further making it less able to hold on to the dye deposits. To be honest, blues like directions turquoise never come out of my hair entirely because it stains (sometimes good, sometimes bad) and work a lot better than permanent dyes. What dye are you thinking of using because there’s very few real permanent dyes in blue.

-What happens if I use semi or demi permanent hair dye on bleached hair (would it go back to the bleached hair color after the dye eventually washes off)?

It depends a lot on your hair and the dye you use. The answer is probably, but there’s never any guarantees as any dye can stain.

-Would I get the light blue color if I had the dye applied on my hair unbleached (mine's pure black)?

You can’t. You can’t get a light colour on dark, it’s a physical impossibility. The dark colour will never allow a light colour to show. You have to bleach first to get it light enough. If the dye is the kind that has peroxide, it’s unlikely to lift your hair enough as you’ll end up with a weird muddy red! 

-How long would the new hair growth take to be about 1/4th of my total hair length after I dye it?

I don’t really understand this question. You’ve not said how long your hair is, but even if I know that, im still not really sure what you’re asking.

-Would you recommend dyeing my hair continually if I wanted to? If not, why so?

With what? It depends on the dye and the reason you’re dying continuously. And what do you mean continuously? Each time you wash your hair? I don’t have enough details to answer I’m afraid! I can say, if it’s a dye that contains peroxide, you really only should do your roots each time and never go back over the lengths.

Thanks for the quick reply 🙂

Actually, I live in a country where hair dyeing isn't really as diverse as in some other developed countries. In fact, most hair dye brands around here sell only shades of black, dark red and brown so more "fun" colors aren't so readily available. In all my online search so far, I've only stumbled upon an imported product called Schwarzkopf Colorworx direct dye that comes in blue, green and other vibrant colors. Again, I'm not really sure how "direct" dyes differ from "normal" dyes so I've refrained from buying it yet. It'd be greatly helpful if you could explain this distinction as well.

So you're saying that permanent dyes would give around the same effect as semi permanent ones on bleached hair? Well that's certainly informative. And what exactly do you mean by "lift" on hair with peroxide dyes?

I'm a male so I keep my hair short to about 2 or 3 inches long. That's why it would be kind of problematic if new hair growth overtakes the dyed hair too quickly. But this is irrelevant to the topic so I'll just leave it at that lol.

Also, by continually I mean that I plan to dye my hair after it has significantly faded for a couple of months consecutively. Is that in any way harmful to hair growth?

Direct dyes or "veggie dyes" are dyes that really just sit on the hair shaft, they stay mostly by staining the hair. Permanent dyes and demi dyes (and some miss-labelled semi dyes) have peroxide in them (normally by mixing it in as you're about to use it as the chemical reaction is quite short time wise, but some are mixed with water and the chemical reaction then effectively makes peroxide). This peroxide has two functions. The main use is to lift the cuticle on the hair shaft to allow the dye molecules into the hair. It also has the effect of lightening the hair (known as lift) which is sometimes desired, but sometimes it's incidental but it's generally a result of using any peroxide. The higher percentage/volume the peroxide the stronger it is, the faster it works and the more lift you are likely to have. Now, it's not as much as bleach (for bleaching you use a bleach powder and peroxide), but it's definitely there.

It's not really that permanent dye will have the same affect, it can be worse, it might be better. But it will damage your hair a lot more meaning it'll be less likely to hold onto the dye. Hair needs to be a little damaged to hold on to the dye, but too damaged and the colour fades fast.

So I understand the length thing now 🙂 It's definitely not irrelevant because it's worth knowing. Basically, in general hair grows around half and inch a month. It might be a little more or less because of genetics, but that's the average. The rule of thumb is to do your roots around every six weeks. This helps to avoid what's known as hot roots, especially when you have dark hair and you're going very light (pale blue needs extremely pale hair, it's not easy!). The heat of your head speeds up the bleach and the further away from your head the bleach is, the further it is from that heat and so it works more slowly. What you tend to end up with is a band of darker hair past the brighter roots. This will affect a colour like pale blue, so you really need to keep it in that sweet spot where it's not too far away from your scalp.

As your hair is going to be quite short, you can get away with more, but using permanent dyes on the same hair over and over really damages it. Do enough damage and it will break off. It won't damage any new growth that comes in, but the bleached hair can break off.

However, if you do manage to get direct dyes, they do no damage at all and you can dye as often as you like! Pale blue does fade very quickly though. You should have a look through this thread on keeping your hair vibrant https://www.hairdyeforum.com/index.php/topic,11009.0.html I wash my hair using conditioner only when I'm trying to keep the colour and use cool water. Doing this I can keep the colour and not have to redye until I bleach my roots. I only use shampoo when I'm trying to fade the colour deliberately!