First, the wood is probably alder. That's what it looks like from here, and alder was commonly used on the bodies of those basses.
I personally wouldn't recommend applying a red stain directly to that body, as it is right now. Although you've sanded off the outer finish, the wood is still filled with sanding sealer down in the grain. And the amount remaining isn't even, as you can see from the various patches of darker tan color. You'll never really get all of the sanding sealer out of the wood unless you sanded off about 1/16" of wood all over every inch of the body. So, you aren't dealing with fresh, bare wood here. Your body has been pre-sealed, or partially pre-sealed, so it isn't really suitable for direct staining.
If you try to apply a stain to it, as it is right now, the color will probably be very blotchy and uneven.
Just to clarify things, the words Stain and Dye get bounced around a lot, and it can get confusing. Dye can often be used to do Staining, and purchased "Stains" can be used as Dyes. The term Dye usually refers to a colored pigment mixed into a solvent or paint base. The Dye, like that bottle that you buy from
Stew-Mac, can be mixed and used to do staining. Or it can be mixed in to some clear finish and applied to make a transparent-colored finish.
When Staining wood, the mixture is very thin, and it soaks into the wood, carrying the pigment (or dye) down into the grain of the wood. Then some kind of clear finish is applied over the top to seal up and protect the wood. This process is usually done on bare, fresh wood. Sometimes a thin wash coat of sealer is applied to the wood first, to help the stain soak in more evenly all over.
Another whole approach is to do a Transparent Finish. That's what that gorgeous red Tele is. In a Transparent Finish, several coats of clear sealer or base are applied first and sanded level. This seals up the grain and provides a good flat surface for the color coats to bond to. Then, some red dye is mixed in with clear finish to make a light transparent red. These color coats are usually sprayed, to get them even, but they can be wiped or brushed. The depth and darkness is built up slowly, in 8-12 coats. Then it's all coated with clear. That's a Transparent Finish. Note that the color (the dye) isn't down in the wood. It's floating in the finish which is sitting on the surface of the wood.
Sometimes, these two methods of finishing are used together. The wood may be stained first in a dark color, and then lightly sanded. This darkens the grain lines. Then, a transparent finish is applied over that to build up the color.
That red J-bass is an example of a stained finish. Notice how it's somewhat blotchy and uneven (although it's still a nice looking bass overall!). It's very difficult to get the color of a stained finish even and as deep-looking as a transparent finish. A bass body, with all of the curves and contours, has areas of end grain, side grain, surface grain, all mixed together, and the color will sink in differently in each area. Add in some partial areas of sealer down in the grain, and it's even worse.
Anyway, my recommendation for your project is to do it as a wipe-on transparent finish, not a stained finish. Tru-Oil is an old classic, although there are other finishes around these days which will dry faster and harder. Start by applying several coats of plain clear to the body, letting it dry and lightly sanding it smooth. Then mix a small amount of the red
Stew-Mac dye into the clear to make a transparent red mix. Don't try to rush it and make it bright red in one coat. Just a little bit of color in the mix, and you build up the red in ten coats or more. That way, you can keep it even, and you will get a lot of depth to the transparent color.
When you get the color where you want it, put several clear coats over the top. Let it dry thoroughly, and lightly sand and steel wool it to the sheen that you want.
Note: Satin sheens and bright colors are kind of opposing forces. High gloss makes bright colors brighter and dark colors deeper. Satin makes them duller. It's really hard to make a bright color satin finish. You can see the difference between that Tele and that J-bass.
I hope this helps.
