.... I can play the boogie walk in G, C, D, E and A but haven't figured out the Bb and F yet ... I am practising the scales! Man that's boring, but I know it's gotta be done so I'll stick with it ...
Howdy Mr. Dawg,
I'm a beginner (8 months) to bluegrass bass playing so I know what you asking about

. I had similar questions and went on a quest to find some answers. Here's some links I found and some advice for what it's worth. Definitely listen to Bobby King is my first advice

! The "Nashville" number system is the ticket to learning not only walking and runs but also transposing songs and tunes into different keys.
Learn the "shape" or pattern for the scales on the bass neck in terms of the numbers. As you do this, notice that there are several "shapes" that can get you the particular scale you working with. OK, now one of the "shapes" that really helped me is the "Nashville H-Pattern" for the most basic major chord walk:
1-3-5-6-1(next octave root)-6-5-3-1 (back where you started).
See here:
http://www.bluegrassbassplace.com/instructional/single_sheet_handout.pdf (graphic takes a bit to load)
If you look at the PDF, you'll see the same "H" pattern for many keys. Bb ain't there but it's just F moved over one string toward the treble G-string side. You can use this pattern a few places up and down the neck. Of course this is for a major key but you could come up with similar patterns for minor keys if you apply the same principles (i.e. learn the shape of the minor key scale and apply the walk pattern).
Here are a few more links referring to walking in bluegrass:
http://www.bluegrassbassplace.com/phpBB/viewtopic.php?t=63
http://www.bluegrassbassplace.com/phpBB/viewtopic.php?t=82
http://www.bluegrassbassplace.com/phpBB/viewtopic.php?t=114
If you are willing to wade through the discussion archives of the Bluegrass Bass Google Group (bgBass-L) at:
http://groups.google.com/group/bgBass-L/topics?start=100
you can find some decent discussions about walking, runs, etc. Search the discussion for "walking" and "runs".
Here are a couple I remember:
http://groups.google.com/group/bgBa...8c?lnk=gst&q=tom+gray&rnum=5#5802bd306cc5458c
http://groups.google.com/group/bgBa...bda3611a830/3d1a1a807f6d79f0#3d1a1a807f6d79f0
http://groups.google.com/group/bgBa...be22e9f809c/a5ef6dc128afd2df#a5ef6dc128afd2df
http://groups.google.com/group/bgBa...538f5bb14?lnk=gst&q=&rnum=64#2f8358f538f5bb14
Bluegrass walking and runs are used with discretion for sure. Not that I really know anything about jazz bass playing but I'm sure the jazzers live for and live by tasteful, soulful, creative walking within fairly complex chord structures in songs and tunes. I ain't there yet

!
I don't know for sure but I think the term "run" is kind of a bluegrass thang based on the famous guitar "G-Run" used by Lester Flatt and about every other flat-picker in bluegrass:
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I'm not sure that jazzers use the term "run" at all. I guess the "run" qualifies to be a "walk" .... it's just a way to get from here (the chord you're in) to there (the chord you're headed toward) in a (usually) scale-related sequence. But what the heck do I know ......
I have a book called "Bluegrass Bass" from 1977 by Alterman and Mintz that talks about walking and runs. They have gotten permission from the original publishers to revise and reprint the book. I think it will be great for us "grassers" when it's done ..... it's in printing now I think:
http://www.bluegrassbassplace.com/phpBB/viewtopic.php?t=207
P.S. Active Bass website also has a "lessons" section, there are some walking lessons / tabs there for practice. Mostly for electric players but you can adapt the lessons for upright:
http://activebass.com/
Also, one of the best lessons on scales for upright bass on the internet that I found was from Rockabillybass.com :
http://www.rockabillybass.com/lessons/SCALESnCHORDS.htm
Have Fun !!!