Bell had 12 carries for 32 yards this season after he was signed in the wake of Matt Forte's ankle injury.
The Bears were impressed with Bell last season as he rushed 79 times for 337 yards and showed flashes, but he they released him in the preseason after he reportedly refused to take a pay cut.
Eldridge was a fifth-round pick in 2010 by the Colts out of Oklahoma. He had 14 catches in two seasons. He was signed by the Rams in May and suspended for the first four games of this season for violating the league policy on performance-enhancing substances, according to NFL.com.
The Chicago Tribune first reported the news.