When we go up for an aliyah then back to our seat in synagogue, we are supposed to go up from the right side of the bimah (as you face it) and back to our seat from the left side. This was how Jews ascended to the altar in Temple days [Zevachim 63a-b]. Also, the entrance to Temple Mount was from the right side [Middot 2:2]
However, I heard that there is another custom: Take the shortest possible route from your seat to the bimah (to signify eagerness to read Torah), and the longest route going back (to signify reluctance to leave the Torah). ("Longest" probably means the longer of left side or right side.)
Which is custom, which is halacha, or do you have a choice?