I live in London, for context, in a heavily hasidic jewish populated area (Stamford Hill). There is a synagogue close by however, If one were to live far from a synagogue but needed to get there on the shabbat and cannot drive, are they able to take the public bus since they are not the one driving it? Does it still count as work being done or interacting with electricity or something of that nature? or would they have to walk to the synagogue

ב"ה Shalom, I answered a similar question 9 years ago titled " Electric Train to Shul" and my answer basically remains the same. Also, on this website Rabbi Sperling wrote about a similar subject and wrote about this issue at length in an answer " Subway on Shabbat" and I concur with what he wrote. See: http://www.yeshiva.co/ask/?id=5356. I will also add now as I had added then. I just wish to add that in the book Tzeda Laderech pg. 113, Rav Yeshayahu Shapira wrote explicitly that one may not travel by train even if driven by a non-Jew , even at the price of praying at home and not at Shul. Furthermore, he added that this has been the custom of all Jewish communities. However, he does point out that in extreme cases as long as the ticket is not being carried on Shabbat or paid for on Shabbat, it has been allowed . Under extreme circumstances, a Rabbi should be consulted again with full details for a proper ruling. It should be clear though, that using a train in such a fashion on Shabbat, is also only if the train does not leave the confines of the city, because if it does even under these circumstances, it would not be allowed due to the issue of "Techumin" which forbids us on Shabbat to go out of the confines of the city more than 960 meters even when simply walking.. (2000 Amot) . What I wrote about a train applies also to a public bus electric or otherwise. All the best