I think it is more the question of how much bacteria then how soon.
When just switching filters, I normally run both together for about a week. If you need the old filter for another tank, split the old media between both filters (I assume both are canisters?). If the old filter has a sponge / floss / pad, rinsing it in the tank is good enough in 'normal' cases.
Courtesy * Integrity * Perseverance * Indominable Spirit * and Self Control
Tenets of TKD