Locked hair can be bleached and/or colored just like unlocked hair. This can be done as soon as your locks can withstand vigorous scrubbing.
Your locks just need to be solid enough that they can withstand the rigorous rinsing and washing required to remove all the coloring chemicals from your hair. You need to be able to rinse and scrub your locks for a minimum of 15 minutes to ensure that all the hair coloring product comes out; otherwise it can remain inside the cores of your locks, where it has the potential to cause long-term damage.
For some people this could be at about 3 months. For some, 6 months. For others, this could be sooner. Use your best judgement. When in doubt, contact a local professional in your area for guidances or services.
For detailed information about how to bleach and color locks, read this guide written by Lish Daelnar.