You could not have a hybrid between a mouthbrooding betta and a bubblenesting betta species. It is practically impossible as the methods of spawning are very dissimilar.
There are bridging species that can alternate between mouthbrooding and bubblenesting (my rutilans and brownorum do) but I don't believe they can successfully hybridise outside of their complex.
I believe Betta splendens can only be crossed with species of the splendens complex, so smaragdina, imbellis and mahachai. However, a cross of these would as someone mentioned probably create a smaller fish, not a bigger one.
I believe it is just selection of larger fish that has led to the creation of giants and king bettas, not hybridising between species.
Also this is me talking from experience. I own mouthbrooders and bubblenesters so I have seen firsthand the differences in courtship and spawning.