You can only bold or italicize if you're using rich text. Make sure you're sending messages in rich (as opposed to plain) text.
Here's an appropriate section from Mail's Help addressing this:
Use plain or rich text in messages
You can use plain text or rich text (HTML) formatting when you write messages. If you receive a message that’s hard to read, you can read it as plain text.
HideIn messages you send
Plain text messages can be read by all recipients, regardless of the mail viewer used. Rich text messages may be unreadable for some recipients because of the formatting used.Set the format for all messages: Choose Mail > Preferences, click Composing, and then choose the format you want to use most often in your messages.
Change the format for your current message: Choose Format > Make Rich Text or Format > Make Plain Text before sending the message.
Set the format for replies: Select the “Use the same message format as the original message” checkbox in the Responding section.