Sponsors say bill is "proactive approach" to preventing more cases of Ebola in U.S.
A security contractor with an alleged criminal history was allowed to ride in an elevator with President Obama on Sept. 16.
The hearing will be the second on Ebola in as many weeks.
The top Dem on the Budget panel called for extra Ebola funding.
Del. Eleanor Holmes Norton (D-D.C.) on Friday requested information from hospitals in the District of Columbia on whether they are prepared to handle Ebola cases.
Sponsor says bill would prevent Ebola from "further infiltrating our homeland."
Twenty-three lawmakers returned to Washington for the Ebola hearing.
Rep. Richard Hanna (R-N.Y.) called for implementing a temporary travel ban on West African countries afflicted by the Ebola outbreak.
Rep. Kenny Marchant (R-Texas) urged the CDC to set up a quarantine station at the airport where a Liberian man infected with Ebola landed last month.
Rep. Michele Bachmann suggests travel restrictions may not be very effective at this point.