I'd like to try a self bow and have narrowed it down to these two.  Which would be easier for a newbie to work with?

Tough choice. I like them both for selfbows. I would say what ever one you could get the cleanest staves from is what I would use first. The straightest with the least amount of twist is what I would work on the first time. Also if you choose mulberry make it a little wider than Osage.

Osage  

Osage is the gold standard, everything else is wanna be's.

Mulberry is OK but often grows with pins in a horizontal line.  This can make it tough to find a bow.  It also is less dense than most osage.  If you can find a good stave, either is fine but osage is better.

You can make a lot of mistakes with osage and still end up with a good bow.

Thank you for your input gentlemen, osage it is!

I'm asked quite often what wood  I would recommend for a beginner and always my answer is osage. As scrub buster said you can make mistakes with hedge you can't make with other woods and still get a serviceable bow from the deal.

Osage. Jawge

Osage and Red Mulberry both are good bow woods.

Red Mulberry is a cousin of osage, and not as dense. Use an osage design on Red Mulberry but make the bow 15-20% wider and you should have no worries.

Red mulberry usually has thicker rings and it can be easier for a beginner to chase rings on it. In my experience, Red Mulberry appears to grow straighter than osage.

Match the right wood to your climate, then match the right design for that wood, and the rest will follow.

Thanks for all the input...be well!

AC