I've ridden to every job I've had over the last 47 years. Do it.

Arlington Texas allows (but doesn't recommend) riding on sidewalks and does not require (but does recommend) helmets for riders over 18 y.o.

You'll need to assess your personal situation and adequately secure your bike while you're at work.

How to lock your bike (properly!) | The Best Bike Lock

If you give us rough starting and ending points of your commute we might be able to suggest a (relatively safer) route.

Fun fact: Arlington Texas is the USA's largest city without any public transportation system.