Yes, you can upload a bootloader to an attiny85-20 from within the digispark environment by selecting whichever kind of programmer you are using in the Programmer menu under tools, then connect the chip to the programmer and select Burn Bootloader. This will install the standard digispark bootloader, but will also disable access to the chip using an ISP programmer, enabling your programs to use the reset pin for whatever. After this, change the "Programmer" back to Digispark and connect the circuit to USB, and see if you can upload a simple program in the usual way.
Arduino ISP will be fine, or you can use a digispark by uploading the LittleWire firmware and connecting every pin from the littlewire digispark directly to the same pin on your hand made digispark, except for pins 3 and 4, which are used for USB between the littlewire and the computer. For LittleWire the programmer you should select is 'USBtinyISP'.
You say "I have all the aforementioned components" but you haven't shown us anything like that. You still haven't fixed your image so anyone but yourself can see it, so I have no idea what is in that picture.