I do not believe it's possible to limit the records retrieved from a geojson file. A complete geojson data structure is always an object, so if you only fetched a part of it (for example using an http range request) then you would get an invalid json syntax - missing either the opening or closing brace and the json would not be parseable by the browser.
I only want the few that should be displayed in the current bounding
OK so this necessitates having a spatial index on the server side, and generate the geojson on the fly to include only the relevant search results. In a PostGIS context, it can be done with a SQL query on point data something like this:
ST_MakeEnvelope(%(minx)s, %(miny)s, %(maxx)s, %(maxy)s, %(srid)s),
Where the minx, miny, etc. parameters are from the leaflet.js getBounds() function which returns the current extent of the viewer. But the implementation would depend on your server-side resources.