Xanathar's Guide To Everything added a clarification on the type of weapons you can use with Pact of the Blade:
If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type.
This raised a further question that was answered by Jeremy Crawford:
Q: So Hex Warrior, the way it is worded has perked up a question for me. Can you have both a bonded regular/magic weapon and a pact weapon gaining the Cha bonus benefit at the same time?
A: The Hex Warrior feature is intentionally worded to extend its benefit to two potential weapons: the weapon you touch and a pact weapon you conjure.
Can I dual wield/hit with two weapons (one touched and one pact)?
Best Answer
Yes
As long as both the weapon you touch and the pact weapon you conjure are light weapons (or you have the Dual Wielder feat), you make make a bonus action when you take an attack action to attack with both weapons.
Hex Warrior states:
So, the only restrictions from Hex Warrier are that the weapon cannot be two handed and you must be proficient.
Pact of the Blade states:
There actually isn't really any weapon restrictions with the Pact of the Blade feature.
So, as long as you use a light weapon for these features (or have the Dual Wielder feat) you can attack with both, one in your primary hand as an action and the other in your off hand as a bonus action.
To allay the concerns you expressed in the first draft of your question, yes, Warlocks do get bonus actions under the same conditions as everybody else:
Since you are using the Two-Weapon Fighting feature of the game, as long as you meet the conditions therein, you are able to take a bonus action.
You do only get one bonus action per turn no matter what, so you cannot attack with both weapons if you've already used that on your turn. But otherwise, Yes you can easily use a bonus action to attack with the weapon you touch and the pact weapon you conjure.