They sometimes do subside but they can also return to the same size.
Get the wart looked at by a dermatologist asap. If necessary have it removed and biopsied for HPV testing. Most people who are exposed to partners with the low risk strains can get warts 2-8 months after exposure. Your wife should get tested yearly or every other year depending on her coverage. The lack of warts on her means nothing. The virus can be made dormant by a healthy immune system but this doesn't mean it won't activate one day when people get ill. Do not have sex with anyone until you know your health by having that bump looked at and if necessary, biopsied.