There's a loreal product called Hi-Color (small black box) that is listed as permanent, it comes in several bright shades of red. no bleaching beforehand, it's all one step. it's sold in pro stores or beauty supply stores, not the regular drug store.

if you use semi-permanent don't bleach to blonde. keep the base color a light auburn, the red will last longer and have more depth. alternately, you can do orange or pink as the base, then add the red on after.

but really, red dyes of any kind always fade fast. you can get things like manic panic or punky color to last significantly longer if you
(1) keep the dye in for 45-60min,
(2) wrap a plastic bag around your head while it's setting,
(3) use heat while it's setting, such as blasting a hair dryer on your head when it's in the bag,
(4) don't wash it every day.

The best red I've found is the Special Effects Nuclear Red. It's a deeper red but it takes a while to fade (don't wash much, use conditioner) and fades into a lighter red instead of a pink or orange.