Shifting right by 2 is correct for getting your byte1 value. You could also floor divide by 4.
For byte2, you can "mask" src using a bitwise AND to get the 2 least significant bits. Then shift left by 6 or multiply by 64 like this:
src = 814
assert src < 1024 # ensure no more than 10 bits in src
w = 8
print(f"{src=:0{w}b}")
byte1a = src >> 2 # right shift by 2
print(f"{byte1a=:0{w}b}")
byte1b = src // 4 # floor divide by 4
print(f"{byte1b=:0{w}b}")
byte2a = (src & 3) << 6 # left shift by 6
print(f"{byte2a=:0{w}b}")
byte2b = (src & 3) * 64 # multiply by 64
print(f"{byte2b=:0{w}b}")
Output:
src=1100101110
byte1a=11001011
byte1b=11001011
byte2a=10000000
byte2b=10000000