Yes, there are various alternate methods of travel depicted in the Star Trek universe which fit the general characteristic of near-instantaneous jumps across interstellar distances. There have been several depicted in the various shows. How many, really depends on how broad your criteria are.
The Spore drive from Star Trek: Discovery
A very close match to the concept of jumping across space is the Spore drive, which is a major part of Star Trek: Discovery. The Spore drive is used across many episodes, both as the focus for the plot and as just a means of transportation. From the point of view of an outside observer, the Spore drive appears very similar to BSG's jumps, even if the technology is explained in a substantially different way. Of the various possible matches for the instantaneous jump technology you're looking for, the Spore drive has gotten the most screen time, by a considerable margin.
Example of a jump using the Spore drive from season 2 episode 2 of Star Trek: Discovery:
Depending on what qualifies for "any near-instantaneous point-to-point travel across interstellar distances", one would have to consider things like:
- the Transwarp beaming which was depicted in Star Trek and Star Trek: Into Darkness, notably in Khan beaming himself from Starfleet Headquarters on Earth to Qo'noS in the Klingon Empire.
- the doorway in the original series episode The City on the Edge of Forever, where jumping through the archway transported you instantaneously not just across light-years of space, but also across time.
However, both of the above examples are on the scale of individuals, rather than ships. If you're interested in only near-instantaneous travel on the scale of space ships, then you'd have to include things like Q instantaneously moving the Enterprise and other ships around in various Star Trek: The Next Generation episodes, etc.