You don't have to switch periodically the switches. Periodically switched capacitors represent resistors with big resistance values. These are used to create high time constants with small device sizes, which makes no sense if you want to design a capacitor bank for a VCO.
For a VCO the tuning range is the minimum-maximum frequency, where you can get the maximum frequency by selecting the smallest capacitance (top branch on your schematic), for minimum frequency you have to select all the capacitance branches at the same time.
Your capacitance values are binary weighted, so with a 4 bit digital code you can sweep the total capacitance value from minimum to maximum in linear steps, and the operating frequency of the VCO will change from maximum to minimum frequency, also in linear steps.
For b0,b1,b2,b3 use DC sources with 0V or VDD, depends on the input digital code.
Point of testing should be that for any 4bit code values from 0001 to 1111 the total capacitance of the bank should change from 1*C to 15*C, and you should check that.