Generally speaking, a few weeks, but it depends on how well you care for your bunnelby and your bunnelby’s personality. Skittish bunnelby will obviously take a little more time to acclimate than those that are more relaxed, and the more you handle your bunnelby in its earliest days, the more skittish it will be (ironically enough).
When you first obtain your bunnelby, take it easy for the first three days. Allow it to become used to its poké ball and, if you’ve given it one, its hutch. Once it seems comfortable in both, begin the gradual process of allowing it to get used to both your home and you. Always let it make the first move; never reach out to grab it unless it’s in danger. Likewise, supply it with plenty of food, water, and distractions as usual, but be present (first at a distance, then gradually closer) as it interacts with these things. With enough care in this manner, it will be easier and quicker for your bunnelby to get used to you.
Of course, spaying and neutering your bunnelby helps too.
The Pokédex According to Bill 