Bicubic2D seems to be exactly meant for this. From the description it looks like it does pretty much the same as my routine, but with a prebuilt command. You may like to compare two plots done with my routine and bicubic2D - I haven't done it but I guess there would be no difference.
Bicubic2D is new in Prime and I was not aware of its existence - I'm a Mathcad 15 user and I plan to stay with that version as long as possible, as Prime is not really a full fledged alternative at the time being. But sometimes one is able to discover an advantage.