Hi Sara and welcome
I would say sooner is better than later. Two females or a male and female are likely to get along. Same-sex pairs usually are best introduced when young and work out best when no birds of the opposite sex are around to create competition. It usually will not matter if it is a WBC or a BHC but if your bird has had a bad experience with one or the other species you might want to get the other. They seem to form opinions about the whole group based on past experiences.
I also have found that birds who were raised around their parents or with siblings are much more accepting of other birds. If either bird was a single chick who was handraised alone or was alone before weaning age it is much less likely they will bond with other birds. It can take days, weeks, months or I have heard some birds taking up to a year to bond with other caiques.
I have had good success introducing year-old birds to newly weaned birds as long as both birds have been raised with siblings or other babies their age.
When I have multiple clutches of birds I will start introducing them once both groups can fly. I can take a few days and up to two weeks. In this scenario, I rarely get a bird who doesn't like the others but it does occasionally happen.
I currently have a 5-year-old female BHC whose history I do not know, and an 8-year-old male BHC who is friendly to other birds. I have been letting them out at the same time and keeping them in a cage with a clear divider between them (they can see but not touch each other). It has been several months. They still do not physically interact but I feel like they both enjoy the company of having the other nearby. They watch one another and will eat at the same time or play independently at the same time. Sometimes they will play with each other with the glass in between but if they are both out the girl runs away if the boy gets within 8-12 inches of her. I don't know how this will end up but I am giving it more time.
Best wishes with your bird
