Maybe. Are you just running the legal 4 watts through the CB? If so, the only problem will be some interference on the scanner (or ham radio, don't know which) while using the CB. If you're running a foot warmer with the CB, you could be looking at some real trouble. I'd move the antennas as far apart as possible to be on the safe side.
You didn't say whether this is base or mobile but in any case vertical separation is MUCH better than horizontal. Visualize the signals coming off the antenna and you'll see why. You don't need much just as long as they're not in the same horizontal plane. Another thing to consider is pattern distortion; CB being HF isn't likely to be as affected as VHF and UHF by a parasitic element in the signal path so I suggest putting the dual band antenna above the CB antenna.
If this is a mobile installation all bets are off. (;->)
Agreed. I too am confused about whether this is mobile or base. You call it a "vertical", which suggests it's a base antenna, but I cannot imagine a need to put two base station antennae one foot apart. Can you clarify for us? Are you talking about a foot of vertical separation or horizontal separation? Vertical separation, not much problem. Horizontal separation, probably a problem.