On a 20-year-old car, almost anything made of plastic or rubber in that cooling system could be leaking, and any plastic or rubber part that has not been replaced in the past decade is about due for replacement.
The fact that your car does not overheat when setting still means that the fan clutch is one of the few parts that is not suspect. Also, I would respectfully disagree with the suggestion to test it with a rolled up newspaper. A 20-year-old plastic fan is really brittle, and the newspaper may snap the blades off.
Places to look for big water leaks:
Hoses - especially the one beneath the intake manifold that is tough to see.
Top radiator hose nipple. If this is starting to leak, the radiator is crumbling from the inside. Replace the radiator ASAP.
The seals between the aluminum core and the plastic end caps on the radiator. If anyone has used DexCool antifreeze, that stuff dissolves that seal.
The external water reservoir. These get brittle and start crumbling inside. As they get old and fail, they let air into the system (causing overheating problems) then they eventually crack on the outside and start leaking.
Places to look for small water leaks:
Your water pump is due for replacement if it has not yet been replaced. It is almost impossible to see the origin of the leak when your water pump fails. The water leaks past the seal and bearing and drips out of the weep hole in the bottom of the water pump. However, you cannot see the weep hole, even with a mirror, until you pull off the water pump. If you have a slow leak and the bottom of your engine is wet with coolant and you cannot see the origin of the water, it is likely the water pump or the thermostat cover.
Thermostat cover. OEM BMW black plastic thermostat covers (the part that the two big radiator hoses connect to) shrink and warp after about 5 years. Whenever you do any major cooling system work, replace the thermostat and the cover while you are in there (not expensive). If you don't want to buy any more thermostat covers, you can get an aluminum thermostat cover as a permanent fix for the plastic thermostat cover problem. Remember that there are two rubber seals, one around the thermostat and one more. Quality thermostats and covers should come with the seals so you don't need to buy them separately.
As for why your car would overheat on the road but not in the garage, my guesses would be:
1) Air in the system. Turn the key on and the heater all the way up to Hot with the car not running. Remove the plastic thumbscrew in the top of the radiator and top off the reservoir until water an no air comes out of the thumbscrew hole. This will leave your reservoir over-filled, so a little coolant will push out the first time you drive the car. Messy, but not a problem. You may have to do this a couple of times to get all the air out. If the air returns, it is sucking in through a leak.
2) Failing plastic impeller vanes on the water pump. If this is the original water pump, your model came with a plastic impeller and it is due for replacement.
3) Plugged radiator. a) The internal water passages can plug up with silicate from cheap antifreeze, or with minerals from hard water. Use BMW coolant (cheaper on line than from dealer) and distilled water. If the radiator is plugged inside, don't bother trying to clean it. You can't. Normally you touch the outside of a radiator looking for hot and cold spots to detect internal plugging, but that is tough to do on this car. b) plugged external air vanes. Radiator external vanes can plug up with dirt, leaves, pet hair, etc. Try shining a flashlight through it or hosing it out from the inside out. If you ever remove your radiator for any reason, take the opportunity to separate the transmission cooler, the AC condenser, and the radiator and hose out the air passages.
P.S. It is not a V6, it is an I6 (inline). Inline six cylinder engines are not as compact as V6 engines, so they are tougher to design a car around, but the I6 is an inherently better design for several reasons. For openers, as I learned in my mechanical vibrations class, an inline six is inherently balanced, while a V6 is very difficult to balance. After many years of work, the designers have a handle on balancing V6s, which is why Toyota was able to switch from I6 to V6 in their pickups and land cruisers, but the I6 is still naturally simpler and longer-lasting, which one of the reasons why BMW uses it.