There is a direct Rebuli bus from GC to Pana and from Pana to GC (I took the latter). There are some posts saying there also is/used to be a direct bus from Pana to Antigua once a day and if there still is then I assume there would also be a direct bus from Antigua to Pana once a day (I think people said at 7 am). The best way to find out is to ask around when you are in Antigua (ask your hotel, ask restaurants, vendors, at the bus terminal...). If there is no direct bus it is either several bus changes or a shuttle. I have done Antigua, Chimaltenango, Los Encuentros, Solola, Pana many times.Edited: 17 July 2018, 13:47
Is doing the long way as fast as taking the direct bus or you would end up spending 5+ hours in the bus?
It usually takes 3 hours or so. There is never a long wait to get on the next bus. When you go from Antigua to Chimal ask the ayudante (or your fellow passengers) to tell you where to get off in Chimal to catch the bus to Los Encuentros. At Los Encuentros you will hear ayudantes shouting Solola or Pana. In Solola get on the bus to Pana. There might be 2-3 buses waiting and all ayudantes will try to tell you to get on their bus. Take the first one in the queue, the one that has people on it as that is the first one to leave (the others will wait till they fill up).
Also, until what time does this busses run?
In Antigua go to the bus terminal behind the market. Ayudantes will be yelling Chimal, Chimal (Chimaltenango). Of course if you would find a bus that goes straight to Los Encuentros that would be even better. The buses start early (5-6 am) and I assume they run till late afternoon but I would want to do it in daylight so I would not start the journey after 3 pm. Your backpack will go on top of the bus. Don't have anything of value in your backpack and keep a small daypack with you with anything of value. I also wear a hidden money belt for passport, cards, cash. Keep some cash handy in a zipped pocket.