From my (limited) experience, watercolours really do need watercolour paper. Even I, a very amateur papercrafter and watercolourist, have noticed significant differences in the way that watercolours move on low-quality watercolour paper vs high-quality watercolour paper. Watercolour paper is very thick, and able to take on the amount of water that is applied. It will not bleed through.
I cut pieces of watercolour paper to regular card size, then attach to a regular cardstock card base - this saves my nice watercolour paper.
Try Canson XL or higher, Strathmore 400 Series or higher, or Arches papers. Some people love this Inkssentials Watercolour paper but I have never used it; others like Strathmore Bristol board. Play around and see the different ways that different papers move watercolours!