I visited Schloss Bürresheim several years ago.
I got there easily enough without a car. Took the train to Mayen and a bus from there. So getting to Bürresheim is basically no different from getting to Eltz. How long it takes of course depends on how far away you are staying...
It is similar to Burg Eltz in that it has been a single-family residence for many centuries. Bürresheim has been occupied by nobles and archbishops and has undergone significant reconstruction and expansion from its original medieval-fortress form; There are numerous rooms, but just a small portion of the original interior is visible today.
Like Burg Eltz, Bürresheim requires a guided tour. I see no mention of language in KGC's post, but AFAIK, unlike Burg Eltz, there is no English-language tour / no English-language pamphlet available for tourists who don't understand German. My German-language tour was interesting, but you'd better have near-native competence to get anything out of it.
So I don't think I have ever recommended Bürresheim to others; I see it as a less-desirable option, basically for two reasons:
1) The language issue
2) The long travel distances from towns/cities where most visitors choose to stay (Cologne and the Middle-Rhine/Mosel towns like Bacharach, Rüdesheim, Cochem, etc.)
Marksburg Castle (true medieval castle near Koblenz) and Burg Eltz are much closer and much more accommodating castle options for most international visitors. As Gundersen points out...
"Most on here will be staying around Cochem or the Boppard/St Goar stretch."
That said... There is an appealing base town which might work well if you really want to see Bürresheim: REMAGEN, south of Bonn on the Rhine River... By public transport, Remagen is...
90 minutes from Bürresheim, 20 minutes from Bonn, 45-50 minutes from Cologne, 70 minutes from Bacharach, and 50 minutes from Braubach (home of Marksburg Castle.)
Remagen is a great town to explore on foot. See Remagen's highlights by leafing through the walking-tour photos which follow. Remagen is also home to the WW II "Peace Museum" at the site of the "Bridge at Remagen."
https://www.remagen.de/Tourismus-Veranstaltungen/Touristische-Highlights/Stadtrundgang/Remagen-Stadt/
https://www.tripadvisor.com/Attractions-g642105-Activities-oa0-Remagen_Rhineland_Palatinate.html