To achieve what I wanted required a different approach:
TextView feedback = (TextView) findViewById(R.id.TextViewSendFeedback);
feedback.setText(Html.fromHtml("<a href=\"mailto:ask@me.it\">Send Feedback</a>"));
feedback.setMovementMethod(LinkMovementMethod.getInstance());
This basically places HTML in the TextView so I get a link saying 'Send Feedback' but clicking it opens the default email application.
Word of warning: Trying this in the emulator didn't initially work for me, saying it was unsupported. This was just because I didn't have an email account setup. Setting one up in the emulator made the link work as I wanted.