Bus from Madrid Airport T4 actually have a stop in front of T3. I recommend to leave here with boarding pass and carry on bag if connecting flight leaves from E gate. There is security check point which was fast. For Priority Pass holders there is a lounge near gate E69.
T2 stop is very close to T3 stop. You can easily walk back there too. T2 has queques for security checks. A chance to save time going through T3 in this case. My flight left from E80.