To me, leap, bound and spring have slightly different emphasis compared with the more neutral noun jump. At least to my ears:

• a leap emphasises the distance, or gymnastic ability of the jump.

• a bound emphasises the energy or perhaps the enthusiasm of the jump.

• a spring emphasises the speed or the unexpectedness of the jump.

So for example, I might use them in the following sentences:

The cat leapt into the air, and landed on the next door neighbour's balcony.

 

When Joe came home, he was met with Bruno the dog, who bounded through the hallway and jumped up to greet him.

 

When Mary stepped on the cat's tail, he sprang up and scratched her.

In the context of your sentence, where the emphasis is on the nimbleness and perhaps distance of the jump, I would therefore choose leap, although I would avoid mixing leap with sprung, instead preferring a more neutral noun to go with the verb leapt or a more neutral verb to go with the noun leap:

In one leap, she jumped up on her desk, nimble like a cat.

 

In one quick movement, she leapt up on her desk, nimble like a cat.

To me, leap, bound and spring have slightly different emphasis compared with the more neutral noun jump. At least to my ears:

• a leap emphasises the distance, or gymnastic ability of the jump.

• a bound emphasises the energy or perhaps the enthusiasm of the jump.

• a spring emphasises the speed or the unexpectedness of the jump.

So for example, I might use them in the following sentences:

The cat leapt into the air, and landed on the next door neighbour's balcony.

When Joe came home, he was met with Bruno the dog, who bounded through the hallway and jumped up to greet him.

When Mary stepped on the cat's tail, he sprang up and scratched her.

In the context of your sentence, where the emphasis is on the nimbleness and perhaps distance of the jump, I would therefore choose leap, although I would avoid mixing leap with sprung, instead preferring a more neutral noun to go with the verb leapt or a more neutral verb to go with the noun leap:

In one leap, she jumped up on her desk, nimble like a cat.

In one quick movement, she leapt up on her desk, nimble like a cat.

In the context of your sentence, you have to use the past-tense form of the verb, i.e. one of the following:

In one leap, she sprang up on her desk, nimble like a cat.

In one leap, she leapt up on her desk, nimble like a cat.

In one leap, she bounded up on her desk, nimble like a cat.

As a native speaker, I would probably use the word leapt in your sentence, since it agrees with the noun leap in the previous clause:

In one leap, she leapt up on her desk, nimble like a cat.

As one final minor change, I would probably change on to onto as well, drop the first comma and change the last comma to a semicolon:

In one leap she leapt up onto her desk; nimble like a cat.

To me, leap, bound and spring have slightly different emphasis compared with the more neutral noun jump. At least to my ears:

• a leap emphasises the distance, or gymnastic ability of the jump.

• a bound emphasises the energy or perhaps the enthusiasm of the jump.

• a spring emphasises the speed or the unexpectedness of the jump.

So for example, I might use them in the following sentences:

The cat leapt into the air, and landed on the next door neighbour's balcony.

When Joe came home, he was met with Bruno the dog, who bounded through the hallway and jumped up to greet him.

When Mary stepped on the cat's tail, he sprang up and scratched her.

In the context of your sentence, where the emphasis is on the nimbleness and perhaps distance of the jump, I would therefore choose leap, although I would avoid mixing leap with sprung, instead preferring a more neutral noun to go with the verb leapt or a more neutral verb to go with the noun leap:

In one leap, she jumped up on her desk, nimble like a cat.

In one quick movement, she leapt up on her desk, nimble like a cat.