Does the size of the data bus control the maximum value the CPU can process?
The size of the data bus only determines how much data can be transferred over the bus at any one instant-- and has no effect outside of that.

The maximum value that a CPU can handle is unlimited for most CPUs, but the max value that can be handled at any one instant is limited (usually) by the width of the ALU, or Arithmetic Logical Unit.  And the ALU width is (usually) the same width as the CPU's internal registers.

The reason why the max value is unlimited is because CPUs can divide up a value into sections, and process each section independently.  We do this when we do math using pencil and paper.  We divide up the numbers into digits of 0 to 9.  CPUs do this by dividing the value into 8, 16, 32, or 64 bit chunks.

Sometimes CPUs will have a data bus width that is narrower than the ALU width.  This is done to reduce the cost of the chip and the memory it is interfacing to.  The original IBM PC used the 8088 CPU which was a 16 bit CPU with an 8-bit data bus.  Even today there are CPUs that do this.  I recently used an ARM 9 CPU that is 32 bits internally and 16 bits on the data bus.  

Other CPU's might have an external data bus that is WIDER than the ALU.  This increases cost but also improves the CPU to RAM bandwidth.

This whole subject goes back to a different question (that nobody has asked), which is:  What does it mean to have an 8, 16, 32, or 64 bit CPU?  The answer is far from simple!  The simple answer to this question is going to be inaccurate and the complex answer is very complex.