Changed path to Bridleway - but still shows up as footpath

The only thing you did wrong, was not having enough patience.

When you save an edit, it ends up in the main database. It then takes one or a few minutes before it gets copied to the rendering database. Next a (re)rendering of the tile needs to be triggered.

If the rerendering doesn't get triggered, you can force it as is explained in this other question. (I've already done that and the path is green now.)

The edit shows as still editing, because saving doesn't close the changeset. You can save often and still be working on the same related set of changes.

Hello (and welcome!). In addition to the "map update delay" issue already mentioned I think that there are a couple of other points worth mentioning:

The first is that in OSM terms the difference between what shows in Potlatch's simple view as "Footpath" (which gets tagged "highway=footway"), Bridleway (which gets tagged as "highway=bridleway") and Cycle Path (which gets tagged as "highway=cycleway") isn't always 100% clear. If you follow the links to the wiki you'll see that different levels of access are implied by these highway tags. If the actual access differs you can add e.g. "bicycle=yes" to a "highway=footway" if that's explicitly allowed.

Another thing is that you'll notice that the bridleway page also mentions the "designation" tag (Potlatch in simple mode calls that "official classification" - here's an example). In England and Wales that's used to record the fact that a path can have a particular legal status such as "Public Bridleway". It makes sense to have a different tag because it's quite common for e.g. farm tracks to be also Public Bridleways or Public Footpaths (here's one, just to the east of Long Wittenham).

You mention "checked on OS map and Oxfordshire definitive rights of way map". Unfortunately most OS maps aren't suitable evidence for tagging within OSM - see this page from the Beginner's Guide for a bit more about this. This excludes OS data that's appropriately openly licensed (such as the OS background map available in Potlatch), but unfortately that doesn't show rights of way. The "Oxfordshire definitive rights of way map" also wouldn't be allowable if was based on OS non-open data (an Oxfordshire native may already know; might be worth asking on the talk-gb mailing list. The easiest way of checking whether you can tag it "designation=public_bridleway" or not is to go there and have a look and see if there's a sign. I've not been along the path in question, although I have walked past the south end of it about four months ago; there wasn't an obvious "bridleway" sign there then.

When I walked past it it looked like either a bridleway or a cycleway to me, although I didn't notice it having a name. I notice that you've given it a name of "Bridleway" which I suspect isn't correct (although there are a few around that actually have a name such as "Bridle Road"). Although the "name" box is quite prominent in Potlatch when adding a footpath or bridleway, you don't have to fill it in if something really doesn't have a name.

It's also worth mentioning that if you're using an external router such as CycleStreets that there will be an additional delay between you changing the data in OSM and it being imported into the CycleStreets router (most external routers display the map data date somewhere; CycleStreets says that they update "several times a week" - currently it's not routing along your bridleway).

Finally (again) welcome! I hope that this helps and isn't too much to take in in one go. Although quite a lot of the footpaths and bridleways in that bit of Oxfordshire have already been added there are a good few that could do with a a local survey - to the north and west of the power station for example.