Sanskrit term for a "Buddhist"
The Sanskrit term for Buddhist is bauddha. 

This derivation is known as a "secondary derivation" (taddhita-pratyaya). An -a suffix is added, and the initial vowel is strengthened. It has the general sense of "of or relating to", and here the specific nuance of "one who follows the Buddha". Compare the more familiar word Jaina, which is the name for a follower of the "Jina", i.e. Mahavira. The word brāhmaṇa is derived from brahman via the same process.