When dealing with that short run before turning, there may be a real problem getting a hose stuck in far enough to really get much pressure on any clog. One of the reallifesavertools, Ihave used is calleda "Drain King".
If not familiar, this is a link to the type gizmo and I might recommend getting one as it makes life much better!
One trick to using one if the drain is too short to get enough in to expand and compress enough to keep water flowing back out is to add a short piece of PVC pipe just on the outside of the drain.
The combo with the amount of the tool you can get into the drain is often enough to get a good seal so that all the watergoes forwarddown the drain asit pullses. The pulses ofwater will often break even the worst clogs. Showers are likely to just be hair and soap scum, so not terrible.
An alternate which might be enough considering the short distance is a Zip-it tool:
Really nice for hair clogs that are often right in the trap or the drain itself as it allows cleaning through the opening without removing any parts on some. Nice small size and flexible to go most any place.