Yes but maybe not in practice
A druid's Wild Shape allows you to “magically assume the shape of a beast that you have seen before.” A half-dragon bear is a beast, but it's between you and your specific DM whether your druid has ever seen one and there's no reason to assume the answer before talking about it. Also, see the section at the end.
Polymorph can do any beast (not limited by what the caster has seen), so it can in theory be used to make a target into a half-dragon bear. True Polymorph isn't limited to beasts and can obviously handle them, too. However, the way it's worded depends on such a creature existing in that reality already, else it doesn't count as a “creature” to validly choose. So on that note, see the section below…
For best results, respect the DM's “character” and your fellow players’ time
Remember that just because something exists in theory doesn't mean it actually exists in a given campaign's world. Since the setting and its denizens is the DM's “character”, forcefully inserting the existence of half-dragon bears into their world may be fine, or may incite anger at your trying to take away the DM's agency.
Being the cause of an argument that derails everyone's entertainment for the evening is not a badge of pride, so to avoid any chance of a derail, talk to your DM outside of the game rather than surprising them with it in the middle of play.