Are drawing an extra card and playing an extra card optional when the Party Bonus rule is in effect?
May is optional.
While I could find no direct rules citation there is this question from the Rabbit Wiki:

Q: When a card states that you &quot;may&quot; play 1 extra card (e.g., Rich Bonus or Party Bonus), and inflation is in play, it is treated as you may play 2 extra cards. Does this mean that you have to choose between playing 0 and playing 2, or can you also play only 1?
A: It's either zero or two. There is no one.

The answer clearly indicates that may is optional.