Giants’ Madison Bumgarner hopes to start throwing in 2 weeks

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Madison Bumgarner is feeling significant improvement and has a date in mind for when he hopes to begin a throwing program.

“I’m shooting for two weeks from Thursday,” Bumgarner said. “That’ll be six weeks out.”

That would be June 1, though it’s possible he could start playing catch at some point in late May.

One sign reaffirming Bumgarner’s improved health is that he’ll be on the Giants’ upcoming trip to St. Louis and Chicago to resume his rehab. He didn’t go on the previous trip (Los Angeles, Cincinnati, New York) because it was too soon after his April 20 dirt-bike accident that left him with a Grade 2 sprain in the AC joint in his left shoulder and bruised ribs.

Of the two injuries, the shoulder ailment obviously is the bigger concern. As for the ribs, Bumgarner said, “I still feel them, for sure, but they’ve gotten quite a bit better.”

The Giants initially said Bumgarner could return to the team shortly after the All-Star break but have since suggested a target of early August, though it’s largely guesswork for now.

Bumgarner wouldn’t predict when he could rejoin the rotation, saying, “I never went through anything like this. We’ll just play it out, really.”

Briefly: The Giants plan to activate closer Mark Melancon (pronator strain) from the disabled list Friday when they open a series in St. Louis. “To rush him before Friday would be a little risky,” manager Bruce Bochy said. ... Infielder Conor Gillaspie will start a rehab assignment Friday at Triple-A Sacramento, and Aaron Hill is rehabbing at Single-A San Jose. ... Bochy plans to rest at least a couple of left-handed hitters with the Dodgers’ Clayton Kershaw pitching the series finale: Denard Span and Brandon Belt, who’s hitting .059 (3-for-51) with 27 strikeouts against Kershaw. “Those numbers are not pretty, let’s be honest,” Bochy said. “It’s a tough matchup for Brandon.”

John Shea is The San Francisco Chronicle’s national baseball writer.

On deck

Wednesday

vs. Dodgers

12:45 p.m. NBCSBA

Kershaw (6-2) vs.

Cueto (4-2)

Thursday

Off

Friday

at Cardinals

5:15 p.m. NBCSBA

Moore (2-4) vs. Wacha (2-1)

Leading off

May power: Buster Posey’s home run Monday was his sixth in May, tying him with Arizona’s Paul Goldschmidt and Philadelphia’s Aaron Altherr for most in the National League this month.

— John Shea