You can find Feebas on Route 1 in the original Black and White games, but it might take you some time. Feebas has a 5% encounter rate while fishing in the water normally, so you shouldn't expect to find it very easily. You will have to be patient with this -- just be glad you're not playing a Gen 3 or 4 game, as the Feebas encounter methods in those games are incredibly strenuous and even more time consuming!
There is an alternative method to encounter Feebas in Route 1, however, which you might find to be a more efficient method. Feebas has a 65% encounter rate when you fish in a spot where there is rippling water, so if you come across one, definitely try this out. Given Feebas' low encounter rate while fishing normally, it might be more efficient to run around for a while until a rippling spot appears in the water, which you can then fish in. There's also a 5% chance of encountering a Milotic through this method, which will allow you to skip Feebas' inconvenient trade evolution.