As a general rule, a debtor's homestead and the eligibility for the exemption are determined by ownership and occupancy on the date that the bankruptcy petition is filed at the court. As always, there could be exceptions to that general rule depending on the facts. The Colorado homestead exemption protects $60,000 of the equity in the home ($90,000 if disabled or 60 years old or more).
The homestead exemption is in rem, not personal. Unlike exemptions for personal property, joint debtors do not get to double the homestead exemption, and a debtor may only claim a pro rata amount of the exemption. For example, a 25% owner-occupant benefits from only 25% of the exemption amount.
Non-exempt equity in a chapter 7 can be used by the bankruptcy trustee to pay creditors. A chapter 13 may be used to protect non-exempt property, which would be at risk in a chapter 7, by paying the non-exempt amount in a chapter 13 plan lasting 3-5 years.
With what's at stake, consulting with an experienced bankruptcy attorney licensed to practice in your state may be a good idea.
You only have to live there (legitimately!) at the time your case is filed. Be forewarned, though, if your property is in Colorado even if you are living there you will have significant non-exempt equity under the Colorado exemption statutes and it could be at risk if you file a chapter 7 bankruptcy case. If you have lived in Colorado for less than two years then other exemption laws may apply which makes the analysis trickier.
You should consult with an experienced bankruptcy attorney before taking any actions you may come to regret.
The last time I checked, the Colorado homestead exemption was $60,000 unless you are elderly or disabled (in which case it's $90,000). So the full answer would appear "until the Colorado legislature amends the homestead law to increase the exemption amount." The federal homestead cap (which kicks in when you've lived somewhere less than 1215 days) would not be factor because the cap is much higher than $120,000.