Can I ask God for success in business?

Yes, and it is worth adding a clause. Ask for the work of your hands to prosper — for customers, for the deal to close. Then ask that it prosper without costing you the things that make prosperity worth having: your honesty, your family, your sleep. What you should not ask for is another person's ruin as the road to your gain. Every prayer here is offered for good, never against anyone. Success asked for cleanly is no lesser prayer.

The old blessing is birkat hamaaseh — a blessing on the work of the hands: not luck falling from the sky, but favor resting on real labor honestly done.

From the sources “Establish the work of our hands upon us; yes, establish the work of our hands.” — Psalm 90