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:
Please read the authentication section of the BigML API documentation for more details.