"Dumb" power from USB
For your particular purpose, you don't need to do anything, just connect GND (black wire) and VBUS (red wire) to your design.

(1) leave D+/D- unconnected;

(2) don't worry about any "low" or "high" power modes. These modes are for host to supervise and police overall power that host believes is available to supply. It never worked correctly. If you don't pull any data wires up, the host will not even know if your cable is even plugged in.

(3) Do not worry much about 10uF limit. In worst case you might get "port overcurrent" message on a host, but it is rare. Or you might disrupt other USB devices that might be working in adjacent ports. But there are plenty of DC-DC converters that use input caps of 10uF or less, so it is advisable to use a better DC-DC converter in your design. If you are not using any DC-DC de-coupling from VBUS supply line, it is a very bad idea for a sensitive analog design.   

Regarding the BC1.2, forget this completely. All you need to care is not to exceed 500mA DC limit. 

Clarification for (2): The OP is not building a USB device. The 100mA is a requirement for USB devices, not hosts. The OP wants to use the port capability of a USB host. Every host port must have an ability to supply 500mA, regardless if there are "low" or "high" powered devices. So 500mA is always fine. If the port will be behind a bus-powered hub, there could be a different story.