[RPG] get improved trip on bard without combat expertise

Yes.

Both penalties are untyped, and therefore stack with each other. You may have a hard time hitting anything, though!

I've played a fighter character up to level 6 with Improved Trip, Combat Reflexes, and a spiked chain. I wasn't overly impressed with the setup. It looks great on paper until you spend all of those attack actions on trip attempts that are straight opposed checks against the enemy's Str or Dex, whichever is higher. Granted, my fighter had a well above-average strength score, but it wasn't other-worldly, so my trip attempts had roughly a 70% chance of success against a foe with no better than average strength and dex. It isn't too often that you get to stand toe-to-toe with an enemy that is average in both of those stats (otherwise that enemy would likely not want to be in melee range with you), so the trip attempts were largely a 50/50 shot. That is far, far worse, than the success rate of just a normal attack, to the point of being very depressing and wasting so many actions on failed attacks.

As for Combat Reflexes with a spiked chain, the extra reach with the chain really enhanced the ability to do attacks of opportunity. However, against any type of smart enemy, one successful lash of the chain on an attack of opportunity severely discouraged other enemies from coming within even the extended range of my character's position, unless the terrain dictated a more close quarters fight. Also, if there are other melee-range allies nearby, smart enemies often could use them as soft cover to avoid provoking my attacks of opportunity at an extended range.

So, all-in-all, the style points are pretty cool, but the practical application of tripping everyone with a spiked chain, even on frequent extended range attacks of opportunity just didn't work out very well.