Bought this car a couple months ago and since i have owned it upon slow acceleration(very little pressure put to the pedal about 10) The acceleration is really shaky, like it jerks forward almost like its trying to shift(but no actual shift just throttle cutout) It does it at any speed from 30 mph to 70 mph upon slow acceleration. Anyone have any ideas on what could be causing this??

misfire? i dont know a bunch about bonneville, but check that first, wires and plugs.

other than that it can be many things.
some member here will help you more.

Common problem with the 4T65EHD trans not just Bonnevilles.
In fact it is the torque convertor and pcm that allows this, if you drop a gear or get into the pedal a bit more the shudder goes away. Most have found this while starting to climb a hill or a steep grade.

A mis would be evident when hard accelerating or high rpm, your description is neither.

Thats the first thing i though was torque convertor/trans unit. Its a more of a surging feeling not a misfiring issue.

Thanks for the info.

This isn't a big concern is it?? Is it best to just push the gas more until it stops??

Most just press through it some shift down.
I have a 3500 stall, almost have to be in 2nd for the feeling to go away around town.

Would a shift kit help the problem??

I like all the above things to check Do you have an SES light? I would do plugs and wires because they are cheap, if you still have it check vaccum lines and then move to trans issues.