Each edition had a different way of doing psionics. There are fans for different kinds of Psion.
I like the 3e Expanded Psionic Handbook Psion. It is moreorless a Wizard using spell points, with a thematic choice of spells.
In 5e, the Bard makes an awesome Psion for prescience (divinination, luck), telepathy (charm, illusion), psychometabolism (shapechange, heal), even psychoportation. Allow Bard to use features without any spell components and focus. The Bard is an awesome Psion as-is, especially for the non-flashy psychic powers.
The Bard lacks telekinesis. If telekinesis is important to the character concept, maybe create a background that grants the Bard spell knowledge. (Compare Strixhaven backgrounds.)
Kinete background
At each new class level, choose one spell from the following list whose spell level you can cast. You know this spell, and can cast it using the spell slots of your spellcasting class.
Mage Hand,
Unseen Servant, Mage Armor, Magic Missile, Shield,
Levitation, Spiritual Weapon,
Fly, Hut,
Freedom of Movement
Wall of Force, Telekinesis.