To clarify things a bit...
Are we discussing starting with the L/R BLEED AIR switches ON as the OP asked, or the PACK/CABIN AIR switch ON?
I have no Lear -40/-45 experience, but in the -30 series the L/R BLEED AIR switches are not normally ever closed by the crew, including during start or shutdown, but the CABIN AIR is turned on prior to takeoff and closed after landing. In the -30 series aircraft, the BLEED AIR SHUTOFF VALVES (SOV) are spring-loaded open and require DC power to close them.
A quick glance at the LR-40 checklist seems to confirm that the L/R BLEED AIR switches, which control the ECS SOVs (opened and closed by DC power) remain on/open during start, but the PACK switch is closed.
So, after all that, I'd say BLEED AIR remains ON, PACK is turned off. Beyond that, I'd guess the reason is to allow the engine to experience cooler ITTs prior to shutdown. Contradictorily, the Challenger 604 directs that the APU or Engines be shutdown with PACKS ON. I believe this is to allow for a more linear temperature decrease for the engine/APU.