What is the best ammo strategy to use in Resident Evil 4 in Professional mode?

Conserving ammunition in RE4 comes down to several things.

Aim for the head (or other vulnerable body part e.g. Tentacles)
Headshots cause the most damage to most types of enemies, more damage = less spent ammunition

Exploit context sensitive attacks
After shooting a Ganados in the head you have the opportunity to kick them in the chest causing a fair amount of damage. Later on in the game, Leon can perform a suplex on enemies after shooting them in the knee. Suplexes cause massive damage, as well as looking awesome, so do them as often as possible.

Hit em while they are down
After knocking an enemy down with a shotgun or a kick you can run up them and slash them with your knife. Balance this with the situation you are in as you may incur damage from being too reckless.

Upgrade your gun's damage as soon as possible
Self explanitory, more damage = less spent ammunition

Do not reload a gun unless you have to
Every time you upgrade a gun's ammunition capacity at the vendor it comes with a fully loaded clip regardless of how many bullets were in there to begin with. Therefore, only upgrade a gun's ammo capacity when the clip is empty.

Specialize your weapons
Each weapon has a role and may not be needed in a level, however, you may need ammunition for that weapon for a future level. In circumstances where you can get by with just your pistol. Store your shotty and just carry your pistol and your magnum in your inventory. This will cause magnum ammo to spawn at a greater rate than if you had a large assortment of guns in your inventory. Then you can store the whole lot at your next sanctuary where you'll need it for the next boss battle.

Use grenades
Like a suplex grenades are effective and awesome. If you can take out 3 or more enemies with a single grenade you are making money.

Buy the RPG
The RPG will save you a ton of ammunition on those difficult boss battles. The one that comes to my mind is that crazy plant child thing.