There are a couple of options available for you: First one being: Embark out of your Titan and quickly shoot the enemy pilot down.
Usually greedy, enemy pilots will try their best to eliminate your Titan for their own gain, giving you opportunity to shoot the enemy down and embark back to your Titan.
If possible: Be surrounded with your friends and teammates.
Usually when looking at your Titan's back, the viewer can notice the enemy on top of your Titan.
This is especially useful if you're on a party or have your mic to communicate with.
Yell out to your teammates to eliminate the enemy rodeoing on you.
Unlocked at level 13:
Use the Electric Smoke tactical ability. Creates a cloud form around your Titan, which generates electricity and hurts those held within the cloud's radius.
Rodeoing pilots, if held on to your Titan and within the electric cloud, will most likely die in this process.
Unlocked at level 24: Use Cluster Rocket/Missile ordnance.
When used, it spreads rockets that injure and should eliminate the enemy on top of your Titan.
However, shoot at a nearby wall/obstacle/enemy, so the clusters of missile could spread wide enough to hit the enemy on your Titan.
gaming.stackexchange.com/users/71300/aonepathan
There are a few options to getting pesky pilots off your back.
hop out and shoot him
manually eject (kills your titan, but doesnt give him any credit for it).
you can also kill him in the air during this because it launches him up as well.
use electric smoke then stand in it.
the pilot will either die or be forced to jump away use cluster missiles on a wall and stand in the explosions (hurts you, but kills him much faster) call out to your team for help
gaming.stackexchange.com/users/47011/Rapitor
Just realized something you can do, have tried in a few games and has been working incredible.
So obviously when they rodeo you they are waiting to see if you're Titan stops moving, which they interpret as you having disembarked.
They can't see in front of the Titan so just have to guess based on the movement.
So what you do is suddenly stop moving, and look down.
They will assume you disembarked, and jump off the Titan to prepare for small arms combat.
Once they jump off.
Dash away, turn around, and blast them.
gaming.stackexchange.com/users/72190/user72190
Something I've found that helps, is to listen for their footsteps.
You'll hear them mounting your titan, banging around above your head.
I've found that if I disembark as soon as I hear them I can often catch them by surprise while they're ripping the cover off my titan.
gaming.stackexchange.com/users/81149/Anonymous
The fastest way I've found, and one I don't see many people using it to get out of your titan and jump kick the pilot.
Instant kill and very little aiming needed.
gaming.stackexchange.com/users/81087/Graham King
A great way to take an enemy off your titan is to get out of it and spam some orndance near it.
Grenades are available from lvl 1 and it's hard to miss your own titan.
gaming.stackexchange.com/users/23901/user1306322
i have played titanfall for a very long time
and i figured that the best way is to use electric smoke and wait for him to hope of then dash backwards to splatter him.:]
gaming.stackexchange.com/users/91467/luke fowler
I have a bit of a problem with hop-ons. These lazy enemy pilots are always hitching rides on my Titan without my permission, and it's beginning to become a nuisance. What can I do to get rid of these freeloading troublemakers?  I don't have an actual screenshot of this happening, but it looks something like this:     Note: Actual rodeo attack may not appear exactly as shown
What can I do to stop an enemy Pilot from rodeoing my Titan?
gaming.stackexchange.com
<titanfall>
gaming.stackexchange.com/questions/160027
gaming.stackexchange.com/users/16793/Brysonic
There are a couple of options available for you:   First one being:  Embark out of your Titan and quickly shoot the enemy pilot down, use the Electric Smoke tactical ability or manually eject. While there are many ways to deal with enemies trying to rodeo a titan, the most common one is to eject and fight.
The community offers some tactics.