Is there a chemical or chemicals that can be infused in fabric that will react when exposed to blood that would produce a bright or glowing color other than red?
Luminol (IUPAC name: 5-Amino-2,3-dihydrophthalazine-1,4-dione) displays chemiluminescence when it is oxidised, and glows a blue colour. It is used in forensic science to detect iron (in haemoglobin) and also to detect copper in biological material.
The process leading to luminol emitting light is explained in this image.
As for whether luminol can be "infused" in fabric, this is difficult to answer, as you have not explained what you mean by "infused". As it is soluble in water, it will easily be washed out, and is thus not suitable for long-term use. Moreover, it will react with a variety of substances (apart from blood), for example bleach.