How do you increase movement speed on the map in Mount & Blade
There are 4 ways that I remember off the top of my head, but I haven't played for a while, so I won't be much more help.
A hero with high pathfinding skill (remember, if you have this skill and your companion also does, you get a bonus)
Smaller party
Extra horses in your inventory
Amount of "infantry" and "mounted" troops, armies with more of the latter move way faster, so there are a lot of benefits of having your army composed entirely of cavalry, not even mentioning how strong it generally is.
Also, Control + Space speeds up in-game time on the world map, whether moving or stationary.
Don't know when this was implemented (works as of Warband 1.134), but I wish I'd had this functionality years ago.