Small aircraft pilot reported a ground conflict with a large jet aircraft while taxiing at LZU airport.

Narrative

I had just refueled at Name (FBO) off of Taxiway B and had received the following taxi clearance: 'Aircraft X; Runway 25; taxi via W'. As I was exiting the FBO and was about to make the right turn from Taxiway B onto Taxiway W; I noticed a Aircraft Y taxiing fairly quickly from West to East just to the West of Taxiway B. Having been issued a clearance without restriction (e.g.; such as to follow the Aircraft Y); I assumed the Aircraft Y would slow down and allow me to merge onto B. Within a split second; I realized that the Aircraft Y wasn't slowing down and that we were on a collision course if no evasive action was taken.To avoid the collision; I braked hard and brought our aircraft to a stop. The Aircraft Y's wingtip passed our nose by only 30-35 ft. Just as I initiated the braking maneuver; ATC called with a transmission similar to: 'Aircraft X; do you see the...' This was meant to point out the Aircraft Y; but as he was transmitting; the controller must have realized that I had come to a complete stop already. He stopped mid-sentence. The lessons from this near-miss for me are:1) Never assume that another aircraft will stop for you; even if you have been given an unrestricted clearance. 2) Remain vigilant of other aircraft at all times.3) Do not assume that ATC will foresee and manage every conflict on the ground. If in doubt; ask ATC for a resolution.4) Once a safe outcome of the operation is in doubt; take immediate and decisive evasive / corrective action.