I'm also a bread baker - weekly - and my answer is.... it depends. I normally work from a poolish, but I've also worked directly from a new yeast starter mixture, which is what you sound as though you're doing.
The "it depends" part is how long do you have before you want to have the bread baked. You can use the normal amount of yeast starter without doubling it IF after working it into your dough you give it time to double again, usually a couple of hours in a warm, damp place.
If you want to work in less time, then there's no reason not to double your yeast.
As I said, I work from a poolish (preferment) that I prepare the night before (1 cup of flour+1 cup of warm water+1 pkg. of yeast. Mix, cover and use it within the next two days.) and guarantees a nice rise in anything I add it to, and I only use one package of yeast to get it started. But in making a poolish, I caution you to use only a glass or ceramic vessel, and stir it with a wooden spoon only. No metal of any kind. Sometimes metal kills yeast. (It has something to do with radical-free ions - remember high school chemistry? I don't. I just take their word for it.) I don't even use plastic.
I hope I've been of some help.