"I aspire to be" is a perfectly correct and usable phrase in written English. You can use it whenever you want to indicate that you hold a goal which you are striving to achieve. For example, "I aspire to be a successful entrepreneur someday."
I aspire to be a better human.
That's what I aspire to be.
"Ben is what I aspire to be".
I aspire to be rich myself.
I aspire to be like her every day.
"This lever represents what I aspire to be".
But I aspire to be a working musician.
"I aspire to be lumped in with Irving Berlin".
"I aspire to be the president of all Venezuelans," Mr. Capriles said.
In my spare time, I aspire to be a wealthy Internet entrepreneur.
"As an artist, I aspire to be as remarkable as Leonardo da Vinci.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union