If, and only if, the project is truly dual licensed then you may pick your preferred license and fork from there. But you must make sure that all aspects of the code that you need are licensed in your preferred license. You are allowed to carve apart a project to ‘cherry pick’ just the aspects you need or are compatible with your preferred license.

Think of the dual-licensing as trim lines on an automobile. Presuming you can only afford one vehicle, you pick one trim line and you drive that off the lot. (Aka, you forked the project.) The vehicle still runs; everything is fine; you have a single license now.

It’s probable that trim line A has some features that you really want, but you can only ‘afford’ trim line B. That’s when you rely upon the auto parts after-market and other mechanics to install the features you wanted from A but couldn’t ‘afford’. And if you’re a truly handy DIY’er, you can make those modifications yourself. Those new features that you built / paid for are now part of trim line B or however you choose to release / license them (this is where the auto analogy falls apart).

Some quick caveats –
1) I use the term ‘afford’ to make the automobile analogy work. It’s a metaphor, that’s all.
2) The license you pick may affect how you can release new features. Using GPL, for example, would force the new features to be GPL’d.

Note, I am not a lawyer.

When a project is dual-licensed it means that you can choose to license the work from the author under either one of the licenses. You are only bound by the one you pick—that is the whole point of dual licensing (though I don’t understand the point of dual-licensing under the GPL and a permissive license). The original code may still be distributed under both licenses by the author, but there is no requirement for you to do such a thing.