Not only can you teleport to the Republic Fleet using your Fleet Pass skill with an 18hr cooldown in your Skills window, but you can buy 1-use fleet passes from the Security Key vendor in Carrick Station, and every planet has a Republic Fleet shuttle in a town somewhere that ports you directly to the fleet.
Fun fact that I found out playing is that there is a pvp vendor for weapons next to the pvp mission box and for their lvl they are awesome weapons. They start at 14 then 24 then it's every 8 lvls. They cost 580 pvp commendations but are will worth the couple hours of pvp time to get. I wish I had know that for my first character.