How long do I have to wait for the next villager to ask me about moving?

You will need to wait 5 days (at a minimum) for someone else to ask to leave. The 15 day wait is only if you say 'yes' to the villager moving out.

The rules around villagers asking to move out, in general, are:

• If it has been 5 days since the last villager asked about moving, and you told them to stay, there's a daily chance (not guaranteed) that another villager will ask about moving.
• If it has been 15 days since the last villager asked about moving, and you let them move/ freed up a plot, there's a daily chance (not guaranteed) that another villager will ask about moving.
• The pool of villagers who asks to move will be limited by some criteria. It cannot be the same person who previously asked to move. It cannot be the person who most recently moved to your island. It also cannot be within 5 days of the villager's birthday.

Source: https://www.polygon.com/platform/amp/2020/5/27/21272128/animal-crossing-new-horizons-villagers-moving-out-data-mine-how-to-acnh-nintendo-switch