Consult docs or other questions on how to add a driver
Here is your "noob" code edited to add a driver. Select a mesh object and run script.
It so happens that the current
context.scene.frame_current is known to the driver namespace as
frame so no driver variable need be created.
ob = bpy.context.object
bend = ob.modifiers.new(name="bend", type='SIMPLE_DEFORM')
bend.deform_method = 'BEND'
fcurve = bend.driver_add("angle")
driver = fcurve.driver
driver.expression = "sin(frame/20)"
Also remember that angles when scripting are natively in radians. 2 pi radians = 360 degrees. So at frame 20 the angle of bend will be sine of 1 radian (or around 57 degrees.) Use
sin(radians(frame) / 20) if frame is expected as degrees.