So this is all a bit tricky particularly if you want to keep everything running. Here are the weird things you need to remember when transitioning. Some are DNS peculiarities, others are WordPress peculiarities, the biggest one being that WordPress unlike MovableType controls the URL rewriting, so even if you point say "tongfamily.com" to the root of your new hoster, if you write in WordPress/Options, the name is "barnaclebill.com", you will always see barnaclebill.com in your web browser when you type tongfamily.com.
Bewarned, that cost me two days!
# It seems to be impossible to move tongfamily.com or any other domain directly because both hosters want control of the domain. So if you leave it with the old hoster (tongfamily.com), then the when you sign up, bluehost.com asks you for the first domain to move and this is both your logon and what is in root.
# WordPress unlike MovableType does rewriting of host names, so in the Option screen of WordPress if you for instance say, the name of the blog is http://tongfamily.richtong.com, then WordPress actually puts in an .htaccess rewrite rule that makes that the name no matter if you come in as tongfamily.com, www.tongfamily.com etc. This is really confusing since you can look at cpanel and think you did it all right, but WordPress is doing the rewriting. Long term this makes sense since you want all access to a single site (whether through www.tongfamily.com, tongfamily.com or tongfamily.richtong.com to look like a single domain name for google. Google doesn't like duplicate data and lowers your page rank otherwise). So, when you do the final move over, remember to switch WordPress otherwise, you will thing it is the domain administration.