In general service, a road would try to use a foreign car for any off-line destination, because they had to pay per diem for the time that car was on their tracks. A car could be loaded for any destination in the direction of the its home road, not just to that road. So, for instance, of your road had a PC car, it could be loaded for anywhere in the direction of PC territory. If no load was available going in that direction, the car could be sent home empty, usually via the same route it took to get to you. Once you returned it to the interchange where you got it, it was that road's problem. For instance, if that PC car had come to you by way of the BN at Wishram, you'd return it empty to the BN at Wishram. The BN then could send it on, empty, or find a load going east.
On the other hand, if you don't have an empty foreign car to be loaded, you can use one of yours, and whatever road it goes to will have to pay YOU per diem. Thus, they'll try to get rid of it as soon as possible, hopefully back to you!
The railroads were very short of good boxcars by the late 70s, which is the reason for the "incentive per diem" cars. Shortlines bought/leased them by the hundreds, just to make the money off their use by other roads. In a few cases, the home roads didn't actually have enough track to hold all of the cars they acquired, if the had all come home at once. In the 80s, the boxcar market was saturated, and many of them DID come home, and were sold to anyone willing to buy them.
In your case, inbound loads could be in anybody's cars. In 1974, a lot of grain still moved by boxcar, with wood or paper grain doors, if any of your customers would be buying carload lots.
Outbound grain, especially at the smaller elevators, would probably be "local" cars, unless the elevator owned/leased their own covered hoppers. In the early 70s, grain cars were often in short supply, and many elevators that wanted the new hoppers couldn't get them. Boxcars were always in short supply during the annual grain rush, and railroads would request that foreign roads return their cars as soon as possible, storing them in yards and sidings for the rush. There were a few leasing companies supplying the new jumbo covered hoppers, but nothing like today, and most grain cars were railroad-owned, or leased to an elevator or elevator group. Those leased cars would be in captive service, so you wouldn't see them at just any elevator. In Pasco, anything except a BN covered hopper was a rare sight in grain service, and was usually a load going to a BN customer.
The result was that, unless your road has a foreign car, empty, and a grain load going in that direction, most of the cars being loaded would probably be yours, or possibly other local roads, especially if there was some type of pooling arrangement for grain service. Given that your road is a bridge line, that would be entirely possible.
Complicating that was that grain service required clean boxcars. That meant not just "sweep the floor", but make sure the interior and floor had no holes or cracks, the car hadn't carried anything that might contaminate the grain, the doors fit well, the roof didn't leak, etc. Grain service boxcars, even if they looked like a plain, weathered 40 ft boxcar, were among the best maintained on the railroads. Grain hauling roads frequently had to shop their grain cars before the rush, to repair damage and neglect from using them in general service the rest of the year.
Summary: In my opinion, inbound loads to mills or export terminals could be in almost any car. Cars loaded at your elevators should be yours, or if your line doesn't have enough cars, cars from your connecting roads. Since the WP wasn't a major grain hauler, this would mean BN and MILW, and possibly UP, since they also ran as far south as Bend, and would serve the terminals in Portland and Puget Sound. Given the way they got to Bend, your line probably has them to deal with as well. Since the BN, MILW, and UP would probably give preference to their own customers in car supply, you'd probably get mostly boxcars, rather than the new, and scarce, covered hoppers, from the connecting roads.