Bulb won't be any different only that you control how long the shutter stays open. You need to pay attention to the exposure. There is one exposure (and its equivalents) for a given scene. If it's bright out and the correct exposure is f/16 at 1/100th second and ISO 100, you can't just open the shutter for 30 seconds using the same f/stop and ISO; it will be totally overexposed (white). You'd have to use a multi-stop ND filter to get the shutter speed down.
Your technique wouldn't have worked with the D3100, either, unless all the scenes were in low light situations. Changing modes will only change what gets the priority. The camera will still select settings to get the correct exposure. If you take over in manual and increase the shutter speed you will only succeed in getting overexposed images.