I think by too bright they're trying to say your colors are a bit blown out. A bit over saturated. Like the whitest part of the left side in the blue is what I would call blown out. There's a difference in going for bright, which is fine to go for, and just going to far and losing colors in saturation. Like on the version you're wearing now if you look at the pink color below the text it's just gone way too far. If the color wasn't so rich or deep or saturated whatever you want to call it then you could have little detail popping up in there.
The colors here are great in their natural state but you've just taken them a bit far is all. If you look at the character it's really just almost hard on the eyes because she's so so bright. You can give the feeling of brightness with colors and lighting etc. but it's the colors themselves that make things bright not over saturating them. The idea and colors are nice it's just like I've said you've just added too much shine frazzle dazzle to them to make them appear brighter.
I went through an old PB of mine and tried to find some examples of what I'm trying to tell you about colors themselves lending to a sig feeling bright without having to over work them. I don't normally post stuff like this but I just want you to be able to see just how colors can be bright but not jarring to the eye I guess?
Also, and this is going to probably contradict what I've said up there, over saturation can be great but in just small small portions. A segment can be boom blown out bright and still work out but if there's just so much in a small sig space that's over the top color wise your eye is going to have a bad time.
The text is really bad too sorry. Keep it simple at first I mean using text in a great way is an art form in itself so use a nice bold font like Aerial or Century Gothic and try to keep the text just straight forward for the time being until you feel you have a grasp on the actual signature part of the design. If you try to just do too much from the start you'll over whelm yourself and you might find it hard to focus on stuff like color and composition.