String height will change significantly. There are three types available. You currently have waht is called exposed core strings, and you may be able to find replacements if you wish. The DRs are what I would call regular strings that are at their full width all the way from the ball end. The third type is something in between. Commonly referred to as taper core they thin and add to the winding over the first couple inches to get up to the full size.
The whole bridge can be adjusted up and down at either side, but not the one or two strings you want to move individually. That sort of change would be accomplished by acquiring new bridge saddles for those positions. If you don't plan to go back to exposed core, then you may just need to carefully file the grooves in the current saddles larger and deeper to accept the full winding strings.
If the current saddles were set up for exposed core strings from the beginning, the grooves won't be large enough for regular strings to sit well. If they are large enough, then the bass was probably set up for regular strings and it will just be a matter of adjusting both sides of the bridge to get where you want to be.
Does that help?