You want to start and finish in DXTbmp because even if the files are in a format recognized by ordinary image processing programs (i.e., 256 color or 32-bit,) if you change the files directly in your image program you'll lose the alpha channel.
So open the texture file in DXTbmp, set DXTbmp to use the image processing program of you choice, reduce the file size, then save through DXTbmp to preserve the alpha channel. (You don't have to shrink the alpha channel; that will happen when you shrink the main texture file.)
It doesn't matter what program you use to do the work. If you don't have anything more sophisticated, Microsoft Paint can do the job. Other programs may (or may not) do a better job of retaining image quality when you reduce the file size.
When you install DXTbmp you can select what program it should use to open texture files. I believe Paint is the default.
If you're just getting DXTbmp for the fist time, don't forget to also grab the related dll files from Martin's site, or else DXTbmp won't work.
In Paint all you have to do is open the texture file, and on the Image menu select Stretch/Skew, then horizontal 50% and vertical 50% and save the changes.
If the textures you're working with don't have an alpha channel it's still a good idea to work in DXTbmp, because then you can be sure that your saved files are in a format recognized by FS. Otherwise, for example, you might open a 32-bit texture file and reduce its size, but when you save it your image program would save it in 24 bit format, which would look the same to you but be invisible to FS.
This is all a lot easier to do than it is to write about!.