You can move resources to a different project at any time. If you want to move resources from one project to another through the BigML Dashboard you will have to select MOVE TO as seen in this image:
It is worth mentioning that when you create a source within a parent project (e.g., Project 1), all the resources created from it (e.g., a dataset, a model, an evaluation, etc.) will be automatically assigned to this parent project (Project 1). Nevertheless, as we have just explained, you can also assign resources to a different project.
If you are using BigML's API you can easily move resources by passing the project/id:
curl "https://bigml.io/source/4f603fe203ce89bb2d000000?$BIGML_AUTH" \
-X PUT \
-d '{"project": "project/54d9553bf0a5ea5fc0000016"}' \
-H 'content-type: application/json'