Based on my testing, it's possible to specify BOLD text within a note by using the API, but not by using the DocuSign web console (UI).
For example, if I submit a "Create Envelope" API request with the following recipients structure -- including a recipient note that specifies BOLD text -- the bold text correctly renders both in the email that the recipient receives, as well as in the Note that's displayed to the recipient when they open the Envelope:
<recipients>
<signers>
<signer>
<email>johnsemail@outlook.com</email>
<name>John Doe</name>
<recipientId>1</recipientId>
<routingOrder>1</routingOrder>
<note>Test note with <b>BOLD text</b>.</note>
<tabs>
<signHereTabs>
<signHere>
<documentId>1</documentId>
<pageNumber>1</pageNumber>
<xPosition>10</xPosition>
<yPosition>100</yPosition>
</signHere>
</signHereTabs>
</tabs>
</signer>
</signers>
</recipients>
However, using that same technique to specify bold text within a Note using the DocuSign web console (UI) doesn't work -- the text is NOT bold in either the email that the recipient receives or in the note they see within the Envelope itself. i.e., here's how I specified the Note via the DocuSign UI:
And here's how it renders both in the email and in the Envelope for the recipient: