What you describe is a case of leaf gall. Those small bumps are caused by an insect that eats or lays eggs on the plant's foliage. Galls are rarely fatal. They may cause early leaf drop, but a healthy, mature tree will be able to cope with such leaf drop by producing new foliage and that a serious problem should only result if the galls keep coming back for several years in a row.

The bad news is that, once you spot these bumps, the damage has already been done. You can't spray to get rid of the bumps that are currently infesting your tree's foliage: you are stuck with them for the present year. If leaf gall is a recurring problem for you, you can spray in early spring to get a jump on the insects. However, do note that you can't just spray willy-nilly: the spray that you use must target the particular insect that is causing the leaf galls to form.

One problem with spraying, however, is that you will be killing beneficial insects, too -- insects that may actually be able to help you control your leaf-gall problem over the long haul (by killing the insects who cause the galls). Spraying is a preventive measure, and that a certified arborist should be employed for the job (because it takes great skill "to identify the gall-producing organism").

The good news, again, is that leaf gall is typically not considered very dangerous (either in general or to river birch trees, specifically). In fact, A leaf studded with these ugly growths is still "usually able to carry out photosynthesis at near normal levels.