I need some help with bleaching!

you need to remove the red first. Use a color remover to get rid of as much of the red as you can; they can be used three times.
Once you have done that, you can see what your base is and proceed to the bleach. If the red was a box (permanent) dye, then you will need to wait a week after the color remover to bleach or it can  reoxidize.
If you need to bleach, you should only do one full bleach process every 4-6 weeks. If you want it done every week, then you will need to do a diluted bleach bath or you can fry your hair. It is also recommended to lather your hair in coconut oil a few hours prior to bleaching.

Wow, didn't know I had to remove the red!! I thought bleaching over it would be just fine, but when I think about it, that's a really bad idea. It'd be a waste, yeah? I have super expensive coconut oil, so that should be fine, but could you recommend a hair color remover on ebay or a site that uses paypal? Preferably a budget option?

Ok, put aside the bleach!

You want to start with a colour remover. If you're in the UK Jo bazz, colour b4 or decolour remover are all good. You can use them up to three times in quick succession.

At the point, take a photo so we can see where you are, then we can advise further.

Edit to add, Oops,  you both got in there quick!

I found this one, and I'm not sure if that's the one you meant? If so, it'd be right in the amount of money I'd be willing to spend to get the hair I'd like!

As for progress, it's as I said- more or less black. Here's a reference just in case!

That is not the Decolour Remover we get in the UK. I am not sure if that is a true colour remover, it sounds like one (they claim it doesn't work by oxidation) but it includes 'oxidizer'. Can you find an ingredients list?

Unfortunately there's no ingredients listed, though I found an alternative (though it's from the same country, not the same seller), and it still seems to have an oxidizer, so I'm not too sure about that.. One question though, I found the Colour B4 remover, and one box is at about 16$. Should I get three for the reapplication in quick succession, or do you need only one box?

One box is enough to cover most peoples hair (I need 1 and a half for all of mine) Whether you will need to do three applications really depends on how well the colour comes out, if you have a lot of build up three may well be necessary, if you have only dyed it once or twice it may be enough to just do it once

Then I'll definitely need to buy three boxes, for three applications, right? I mean.. I have a lot of buildup. Like.. a year and a half's worth.

It depends how easily it comes out tbh. Better to have some spare, than not have enough, it is much safer than trying to bleach out colour

I would get three as darker color can reoxidize so having spares is good.