It seems to only happen fairly infrequently in urgent cases; if the bill isn’t urgent, the President either waits out the 10-day veto period, or just revokes the White House legislative clerks’ ability to have bills presented to them while he is overseas, meaning the 10-day period can’t begin at all. This 1977 memorandum from the Office of Legal Counsel states that the first course of action is to agree with congressional leaders to postpone the passage of bills until his return. It goes on:
In the unlikely event that the President is unable to obtain such a commitment from Congress, including the contingency of urgent legislation that cannot await the President’s return, the President normally withdraws the legislative clerks’ authority to accept enrolled bills on his behalf when he travels abroad and so advises the Congress. The bills are received by the White House staff not for “presentation” to the President but for forwarding or transmission to the President. Presentation is then effected either when the bills actually are received by him abroad or upon his return to Washington.
I don’t think a full list has been published previously; to do so you’d need to match up the date each bill received a signature with the published dates a President was overseas.
During President Obama’s tenure, the practice was that while the President was overseas for the passage of sufficiently urgent bills, an autopen device was used to simulate the President’s signature on bills after his permission was given remotely.
For example, in 2011, the autopen was used to extend the Patriot Act while Obama was visiting France, and on another occasion when Obama was in Malaysia in 2015, the device was used to sign the Surface Transportation Extension Act of 2015, Part II - according to USA Today. Most sources I’ve seen seem to put the number of bills signed in this way at 7, but I haven’t seen a source which fully enumerates them.
This was, however, the first time such a device was used. Despite the Obama administration relying on a Bush-era memorandum which advised that the use of the device fulfilled the constitutional signing requirement, President Bush never actually used an autopen himself. The memorandum does note, however, two previous occasions on which the OLC advised that a bill should be flown to the President for signing:
Indeed, on at least two occasions, a bill was flown halfway around the world, on the advice of this Office, so that the President could personally affix his signature to it. See Tarr Memorandum at 9 (China); see also Memorandum for the Files, from Jeffrey P. Singdahlsen, Attorney-Adviser, Office of Legal Counsel, Re: Preliminary Advice and Consideration Regarding Proposal to Fax Continuing Resolution to the President While He Was Abroad at 1 (Dec. 22, 1999) (Turkey).
I haven’t been able to find the specific memoranda referred to, but I’m pretty sure the bills referred to are S.2570 - A bill to continue the transition provisions of the Bankruptcy Act until May 26, 1984, and for other purposes, signed by President Reagan during a state visit to China, and H.J.Res.80 - Making further continuing appropriations for the fiscal year 2000, and for other purposes, signed on November 18th when President Clinton was in Turkey for a state visit.
From Obama's use of the autopen until now, there have only been two further bills signed while overseas; President Trump signed H.R.2157 - Additional Supplemental Appropriations for Disaster Relief Act, 2019 aboard Air Force One, en route from France to Ireland, according to the 2019 Digest of Other White House Announcements. More recently, on October 31st, 2021, President Biden personally signed the Further Surface Transportation Extension Act, while attending a G20 summit in Rome.