With a bit of text processing (maybe in Excel), you can bring your data into this form:
Duration;user;wkt
298;Casual;LINESTRING(-77.0444 38.9101,-77.03818 38.91554)
which can be interpreted by QGIS as well known text (WKT) using Add delimited text layer
.
Note that you need blanks and comma as delimiters for lon&lat values and linestring members, and lon values have to be first. In the dialogue, only check semicolon as column delimiter.
Applying EPSG:4326
as CRS , you end up at New Hampshire Avenue Nordwest in Washington DC.
EDIT
this one works from your second example:
seconds-total;Subscription-Type;gis-data
298;Casual;LINESTRING(-77.0444 38.9101,-77.03818 38.91554)
27926;Casual;LINESTRING(-77.0444 38.9101,-77.03818 38.91554)
214;Casual;LINESTRING(-77.0511 38.8573,-77.051516 38.848441)
960;Subscriber;LINESTRING(-77.024649 38.936043,-77.012289 38.915417)
378;Subscriber;LINESTRING(-77.04062 38.917761,-77.0471 38.9054)
2085;Subscriber;LINESTRING(-77.041606 38.904742,-76.9862 38.8803)
441;Subscriber;LINESTRING(-77.094875 38.88786,-77.10108 38.884616)
456;Subscriber;LINESTRING(-77.023086 38.8997,-77.022155 38.912719)