You need to get a book on coding and take step by step because the fact that you are this lost you need to take a step back and get something that will teach you step by step.
double angle = 180.0 / 3.14 * Math.Atan(bug.getPos()-> bug.getVel().Y, bug.getPos()->bug.getVel().X);
Why are you putting in position when my code takes atan(velocityY/velocityX). You threw in 2 extra pieces of data and then called the positions as if they are pointers?
You also need to look up the C sharp Atan function and see if it gives radians or degrees. With radians you need the 180/3.14, with degrees you don't. If you still have trouble, then spend a few bucks and buy a used C# book.
I'd down vote you if I could. He's asking a math question, not a programming question. The only thing he's done wrong here is post in the wrong forum.
I'll point out, I'm not a math wiz, so my terminology is probably off, but you should get the idea, and I'm assuming you want this all to be in 2D.
Now lets assume, the angle were going to be facing in is in radians (not degrees), and vec2 is a structure with a x and a y value.
Vec2 charPosition; // = the character we what to face towards our target.
Vec2 targetPosition; // = what were are trying to look at.
// to calculate the angle or character needs to be at to face the target.
angle = atan2(targetPosition.y - charPosition.y, targetPosition.x - charPosition.y);
// now if you want to find out how much on either axis you should move each step
xVelocity = cos(angle);
yVelocity = sin(angle);
// You would then normalize those velocities and multiply them by the frame delta, and your desired velocity per second.
Once again, this assume your angle is in radians, and that atan2, cos and sin deal with radians. They do in C++, but you should verify they do in C# aswell.