You can find your credentials to access BigML in several places. On the one hand, your BigML username is always visible from the BigML Dashboard, as shown below.
On the other hand, if you prefer to work with BigML programmatically, you will need your API key, which can be found either in your settings account or clicking the configuration icon on the top widget, as shown in the image below: When you click the configuration icon a small window will display with your API key details:
Those credentials will allow access to your personal workspace. Please read the authentication section of the BigML API documentation for more details.
BigML Organization access
If you are a member of a BigML Organization, you might also need to specify the Project ID to access the resources therein or the Organization ID to access the Projects that you are allowed to work with. This information is available clicking the same API key and resource/id icon that appears in the Organization workspace.