Why does my Query use a Bitmap Heap Scan
It is doubtful whether this query needs speeding up, but if anything can improve the performance, it would be
CREATE INDEX ON connections (host_name, epoch_time) INCLUDE (connections);

This assumes that there is actually a column connections; if that is a whole-row reference, you cannot get an index-only scan.
Make sure the table is vacuumed often.
Also, bear in mind that each index slows down data modifications. So use it only if query speed is paramount.