Asking people whether they prefer to receive HTML or text emails is definitely a best practice, and the best way to do this is to ask for any necessary contact information during the initial email sign up. If this is not possible, some organizations send out an email to their base that asks, "How do you prefer to get your emails?" with a link to their update page, which sounds like what you want to do. Usually there is a very low response rate, but you can continue the "ask" in future emails as well.

In terms of offering a “bribe”....

1. Know your audience! Its encouraging to find reports or generalizations that support a strategy you're trying out, but the best way to know if a strategy will work is to really understand who you're trying to reach. Some audiences might feel manipulated by some sort of bribe, and some might love it. Check out Aspiration's slidedecks on Website Audience and Goals, most of the information applies to email audiences as well.
2. In general, any time you are uncertain about an email strategy, you can and should test your idea on a small population to see how people respond to this. Email Blasting tools are great for helping you segment your lists and analyze results such as who is opening your emails in the first place and who is clicking on the content. For examples of these, check out Popular Bulk Email Tools on Social Source Commons. In this case, you could try the “bribe” out on a small segment of your email subscribers and see how they respond. Alternatively, you could try out two different bribes and see if one works better.
3. Always ask yourself, "What's in it for them (constituents, users, subscribers) to take action or make an update?" A common email update "bribe" or "value-add" is asking subscribers to update the information so an organization can provide tailored newsletters based on where you live or what you like
4. The more honest you are about your intentions, the better. Be careful that any "bribe" offers value to your users and builds on a trust relationship. Only ask for information that is critical to your campaigns. If you require a lot of information about a person to sign up to your email newsletters, the less responders you will get because you are increasing the barrier to participation. Increase the value for your subscribers of updating their information, and let them know this!

For more ideas on how to get people to respond over email, check out these resources:

• What makes an effective or compelling subject line?, Answr
• 10 Steps to a Great Email, Mal Warwick Association
• Building Online Community Through Email Noodges, NTEN