The bridge is where the sound is channeled and focused in an upright. The body of the bass amplifies and adds resonances. In general a bridge-mounted pickup will give you a more uprighty type of sound. AFAIK this is because using a pickup that senses the string between the bridge and where it is stopped will always result in comb filtering.
While a bridge-mounted pickup will capture more uprighty string vibrations, there is no way to accurately capture the decay characteristics and resonances of the upright's body. An ABG or hallow body bass will have resonances that sound nice, but they will tend to be at a higher frequency, which can give the sound sort of a toy-like or artifical quality.
Marcustico ABG:
Success really depends on what aspect of double bass tone you are trying to capture. To get a more authentic dynamic note envelope, you could try some sort of material under the strings to function as mutes. Mutes will shorten decay and dampen harmonics. However, IME, mutes may make one range better in some way and another range worse to unusable. For example, adjusting the mute for the right decay near the nut and it may cause notes higher on the fingerboard to sound pinched.
Tapes are probably the way to go.