The bottler is the man or woman who passes round a collecting box or bag during or after a performance.
The money was at one time collected in a leather "bottle" - ie a leather receptacle which was bottle-shaped, with a narrow opening and a bulbous bottom. This allowed coins to be dropped in, but the only way to get them out was to turn the bottle upside down and shake vigorously. In this way punters could not extract coins in the pretense of contributing - and the bottler could not slip a few coins in his pocket since the showman inside the booth would hear him shaking the bottle. You got a similar idea with wooden church collecting boxes with a slotted top - and of course child's slotted money boxes.