It was a violation of the Torah to travel from one city to another on the Sabbath. The Torah says one must remain inside their "camp" on the Sabbath. Exodus/Shemot 16:29 "the L-RD hath given to you the sabbath...no one doth go out from his place on the seventh day.'" On a normal Sabbath Day, it would have been a violation of the Sabbath to travel from Bethany to Jerusalem. Some people think the ban was the "Sabbath day's journey", but one could actually walk around all day on the Sabbath if there was a spiritual reason to do so, as long as he remained inside the "camp". He just couldn't go more than a "Sabbath Day's journey" outside the camp. No two cities could be within a Sabbath Day's journey of each other either, due to how the definition of a Sabbath Day's journey is derived.

The following graph shows how the boundaries of a city were laid out (see Num 35:1-8).

One could travel to the edge of the pasturelands, but not beyond on the Sabbath. The pasturelands beyond the city walls were considered part of the "camp". This is where the measurement of 2,000 cubits for "Sabbath Day's journey" came from - one could go this far outside the city, but no farther.

Now the Sabbath day's journey was doubled at some point and about double this by first century AD for reasons that weren't scripturally based.

Now during Passover, many tents would be pitched outside the city walls of Jerusalem for visitors. Thus, a new "city wall" could be considered to have formed along the line of tents. Jerusalem had temporarily expanded on Passover, in a sense. So I guess it's possible that during that period, it's possible the 2,000 cubits would have been measured from the outskirts of the most distant tent still within the original 2,000 cubits of the city walls. (And by this time the Rabbinate had expanded the distance to twice this distance.)

Now with Bethany a little under 2 miles from Jerusalem, city wall to city wall, as the map below shows, their 2,000 cubit extension comes within 2,000 cubits of touching during normal periods...

As shown above, the Mount of Olives is just to the East of Jerusalem, and Bethany is at the Southeastern slope of the Mount of Olives. Now during Passover week, the population of Jerusalem would swell from a normal of 600,000 during Y'shua's time to 2-3 million. They would pitch tents outside the city, as illustrated by the triangular shapes below.

Some have theorized that the 2,000 cubits, during this period, would be measured from the edge of the tents, not from the city walls. In the wilderness, where there were no city walls, it was measured from the tentline. This would expand the "common areas" to overlap with the common areas of Bethany, theoretically making them a single encampment during the Passover/Hag Matzah period, and thereby making it OK to travel from one city to the other on the Sabbath since they were at that point a single encampment.

The exact meaning of "Bethany" is a bit obscure. Some say it means "House of dates" because of the abundance of fruit growing on trees in it's area. Others translate it as "House of Affliction" or "House of Poverty". If you take the latter (which I consider more likely), the map above provides an interesting mental image since it means that Bethany (possibly meaning House of Affliction) and Jerusalem (City of Peace) were one and the same "encampment" during Passover week! By His stripes, indeed we were healed!!! And it would also mean that it's only because of the Passover sacrifice He made of Himself that we can travel from our own House of Affliction to His City of Peace. Amen!