Yes, you can just add it all together at once. It's commonly taught that the first thing you do is the deprotonation, then the anion attacks the nucleophile. In many systems this isn't the case, especially with amines. Amines are so reactive that they usually donate their lone pair first, creating an ammonium cation. This then gets deprotonated by your base. Essentially, it works in reverse of what is often taught in organic chemistry courses.
Sodium bicarbonate is too weak of a base. If you're going to use it here you'd want sodium carbonate. However, the solubility of it in organic solvents is pretty limited, so you'd have to use a solvent like DMF, which is a pain in the ass to get rid of at the end. Just use pyridine or triethylamine in dichloromethane. If you're nervous about it try it at a very small scale to see if you get product. Then if it works you can scale it up. But I did an isocyanate to urea synthesis just a couple weeks ago using these conditions and it worked fine.