yo!
I suggest having the Bronco checked for Diagnstic Trouble Codes (DTCs) for Free at a local parts shop;
Have all lights & Accessories Off.
Be sure that they do the KOEO = Key On Engine Off portion first;
then, engine @ Normal Operating Temperature before doing the KEY ON ENGINE RUNNING (KOER) portion
Post any DTCs found here and then we'll see what other tests are involved
Is that shift to 3rd Hard or Soft?
Is the Transmission Control Indicator Lamp (TCIL - LED @ end of shofter stalk) Flashing?
Some poss."
Delayed or No second-to-third Upshifts may be caused by fluid leaking past the transmission Accumulator Seat (TSB No. 99-9-6, May '99) Source: by CanadianDriver.com
& (incl for a typical accum. issue and delayed/late shifts) Late 1-2 Upshift; "...Accumulator Body Problems; The small valve indicated in the picture above will wear the hole causing the small valve to stick partially open. When the valve would stick, it caused a late 1-2 upshift, you actually had to let up on the throttle for it to shift, then all of the other shifts were perfect. We spent hours checking the TPS Sensor, PCM..."
Source: by specialtytrans.com
GL!