Building on user1118321's answer:

I checked the manuals for the following cameras to which I have access (in order from earliest to most recent release):

• EOS 5D Mark II
• EOS 50D
• EOS 7D
• EOS 5D Mark III
• EOS 7D Mark II

All of them are near identical to the 70D's manual with regard to AEB. The first four cameras on the list above were released before the 70D, the last was released after the 70D.

I checked each one of the camera's listed above to see if they allow AEB in M exposure mode. They all do. The option for Exposure compensation is greyed out when in M mode for the ones that do not allow 'Auto ISO' in M mode, but AEB can be set and used. I'd be extremely surprised if your 70D wasn't the same.

To take all three images with a single shutter press, set the camera's drive mode to High Speed Continuous or Low Speed Continuous mode and hold the shutter button down until all bracketed images have been taken. A wired cable release works very well for this. You can also use the self timer to take the entire series after a single press of the shutter button after a 2 second or 10 second interval.

If the camera is set to Single Shot, a separate shutter press will be required for each frame. The Exposure Lock symbol will blink in the viewfinder and on the top LCD panel to indicate exposure is locked at the selected intervals for the series.