Saint Martha is the only Dragon Rider (True) in Fate/Grand Order.
Martha is the only servant to hold the Riding skill rank of A++ which is the highest known rank of the skill and the required parameter ranking to ride a True Dragonkin.
From Martha's profile in Fate/Grand Order, Complete Materials I:
>Riding: A++
>It is possible for Martha, who materialized as a Rider, to freely handle all vehicles and beasts
>In addition, regarding the Dragon Kind, it should originally not be possible for one to manage them with the Riding Skill, but it is exceptionally possible for Martha to ride them
There are other servants in Fate/Grand Order that ride dragons in some forms.
Jannu Alter can use her Dragon Witch skill to take control of certain dragons. Quetzalcoatl can summon and ride her Winged Serpents Quetzalcoatlus. Ryouma can ride and fly on top of Oryou-san etc.
However, those are not True Dragonkin like Tarasque and these servants are not riding them because of the ranking of their Riding skill, but due to them being part of their skills or Noble Phantasms.
There are servants with Riding skill at a rank of EX, but that ranking doesn't necessarily mean it's better, and wouldn't necessarily allow the servant to mount and ride a True Dragonkin who are the pinnacle of Phantasmal Beasts Species. The EX ranking of the Riding skill can mean different things for each servant, like Mysterious Heroine X being able to pilot a spaceship, Summer Frankenstein being able to ride Motor-Babbage, Cinderella Liz being able to ride in her Pumpkin Carriage etc.
Tarasque (who is reported to be the son of Leviathan as written down in the Old Testament) is one of the very few True Dragonkin that we know in the franchise. Martha's ability to tame and ride a True Dragonkin is tied to her legend in life and is reflected in her Riding skill's rank being the highest, at A++ which no other servant has and is what makes her the only Dragon Rider (True) in the game.