My advice is try not to always think of literal notes and instead think of numbers. Walking patterns can be thought of like this: 1-3-5-3 , 1-3-5-6, 1-3-5-6-b7-6-5-3 , 1-2-b3-3-4-6-b7-7, .....etc. You take any note as a root, and then build the lines using the same intervals. So, 1-3-5-6 in F is: F-A-C-D; in Bb: Bb-D-F-G...etc. If you learn to think of lines and chord progressions in this way, changing keys becomes much easier.