In The Phantom Menace, we see the Jedi free a large crew, much larger than needed for that ship. Why didn't they get an escort of fighters piloted by some of the people they freed?
The rescued pilots and ground crew (led by Sio Bibble) went to secure the hangar against droid reinforcements who might prevent the Queen's ship from escaping. We can assume that at least some were captured alive since we see Bibble in a later scene.
Per the official novelisation
On the far side of the hangar, Obi-Wan Kenobi launched himself at the battle droids holding the Naboo pilots hostage, cutting into them with ferocious determination. Qui-Gon watched his progress, long hair flying out as he withstood yet another rush from the battle droids attempting to reclaim the Queen’s transport, blocking their laser bolts as he fought to hold the boarding ramp. Obi-Wan was running toward him now, a handful of the Naboo in tow. Explosions rose all around them, deadly laser fire burning into metal and flesh. Several of the Naboo went down, but the battle droids were unable to slow the Jedi.
Qui-Gon called sharply to Obi-Wan as he went past, telling him to get the ship in the air. More battle droids were appearing at the hangar doors, weapons firing. Qui-Gon backed quickly up the loading ramp and into the transport’s dimly lit interior. The ramp rose behind him and closed with a soft whoosh.
Per the film script.
The DROID GUARD draws his weapon, but before any of the DROIDS can fire, they are cut down. OTHER GUARDS run to their aid. OBI-WAN attacks the GUARDS around the PILOTS. QUI-GON stands, fighting off DROIDS as the OTHERS rush on board the spacecraft. OBI-WAN, the FREED PILOTS (including RIC OLIE), GUARDS and GROUND CREW MEMBERS rush on board the ship. The OTHER PILOTS and GUARDS race to SIO BIBBL[E]. After everyone has made it onto the ship, QUI-GON jumps on board. ALARMS sound. MORE DROIDS rush into the hanger and fire as the ship takes off.
The Junior Novelisation (always an upbeat version of events) indicates that some simply escaped via the exits.
“You’re under arrest,” the droid said. As it raised its blaster, Qui-Gon cut it down. The Queen and her handmaidens ran past him and up the boarding ramp. More battle droids converged on the ramp. Some of them fired as they came, so that Qui-Gon had to parry the shots in between chopping battle droids in half. More shots sounded from the corner. Most of the pilots and ground crew ran for the exits; Obi-Wan and one of the pilots made for the royal spaceship. Belatedly, alarms rang through the hangar. As soon as he was certain that everyone was safe, Qui-Gon disposed of his last few opponents and leaped up the ramp.
While it's uncertain if this holds up in current canon materials, it seems the intent at the time was that they either weren't equipped with hyperdrives, or if they were, they were short range and not capable of the long trip to the core worlds without refueling.
Hyperdrive-capable starfighters are naturally limited by fuel capacity to jumps of less than 1,000 light-years. Previously, Naboo N-1 fighters operating far from home could only travel in small steps, accompanied by a tanker. After the invasion of Naboo, designers added innovative recharge sockets to the wings of the new diplomatic barge, thereby enabling the ship to carry it's own security escort through hyperspace.
So the clear implication is that the Naboo Royal Starship featured in TPM didn't have this feature and that any fighters that attempted to run the blockade with them (assuming they survived) would have very quickly fallen behind and become stranded.
From a more tactical standpoint: there's not a lot a few fighters could have done them anyway. The goal was to clear the blockade, and once in hyperspace they would (in theory) be out of immediate danger enroute to Coruscant.