General Disruption:
* Interfere
* Interrupt
* Disrupt
* Bother
* Upset
* Trouble
* Agitate
* Perturb
* Discompose
* Inconvenience
Mental or Emotional Disturbance:
* Annoy
* Irritate
* Vex
* Harass
* Alarm
* Frighten
* Scare
* Unnerve
* Distress
Physical Disturbance:
* Move
* Shift
* Shake
* Stir
* Dislodge
To Make Someone Uncomfortable:
* Offend
* Insult
* Embarrass
* Humiliate
To Mess Up or Disorder:
* Scatter
* Disarray
* Disorganize
* Confuse
The best synonym for "disturb" will depend on the specific context of your sentence.