You can definitely go from blonde to red. There are a few things you should know...
1) depending upon how light the blonde is and how porous the hair is, a bright red color applied straight over top could take on an unnatural pinkish or orangeish hue. With that in mind, choose a shade of red that also has some brown in it. Or buy a brown shade of the same type of haircolor and mix it with your red. Or (as with a professional 'color back' process) fill the hair beforehand and then tone over top of it with a brownish shade. Either way, you'll need the brown.
2) Red pigments are the quickest to fade because of the tiny size of a red haircolor molecule. You can easily touch up your color after a few weeks. Or use a pigmented shampoo and (most importantly) conditioner that will deposit a bit of red pigment each time you wash/condition. And try to use water that is on the cooler side to wash/rinse your hair. Hot water will open the cuticle (outer) layer of the hair and make it easier for your color pigments to wash away! Always give a cool rinse at the very end to close down that cuticle layer.