Your intuition is right: yes! As professionals, it's their job to be nice. They might feel something for you. However their professional boundaries force them to simply not cross the line.
If they take a step and respond to your invitation it could bring trouble to their business and reputation.
Suppose you really fall for your personal trainer.
Is he married or already committed to someone? Find this out ASAP.
Now that we know the objections, let's find a way to get around them: meet him outside of his professional context. Where does he hang out? Give him clear signs you like him. Smile. Slightly sustain eye contact. Find out if you like the guy outside of his professional context.
Shift roles from professional-client to man-woman.
Flirting is a natural way of being, so don't be afraid of flirting and expressing yourself, being sexy, even when he sees you professionally. Love is a natural stream! Express it! Let it radiate. Have fun with it. It wakes up your senses, wakes up your desires and excitement. It is a great gift! Follow your instinct!
You can say "I like you" in so many ways: watch your body language, your posture, your looks, the tone of your voice. Be confident. Eat him with your eyes! Wake up his senses!
Listen to his response. Don't make him feel uncomfortable. Again, the best is to connect with him outside of the professional context, that way, things are 100% clearer.