I am female, over 60/concerned that the fleshy part of my external urethra is a bright red. What causes this? I do not have a UTI or yeast infection.

May be a caruncle... What you described most likely represents the occurrence of urethral caruncle - a 0.5-1 cm papular lesion from protrusion of posterior aspect of urethra, which is benign & usually asymptomatic, occurs to menopausal women, and requires no Rx, but occasionally still needs some Rx to shrink it or remove or biopsy it. Detail? Ask urologist timely.