Is there a definition of "bipartisan support"? For the Senate in the US, when can you claim a bill was supported/passed by bipartisanship, and when you can't claim thus?
This is entirely dependent on the speaker. But in general senior politicians who have passed legislation are happy to call it Bipartisan on the basis on a single vote.
Nancy Pelosi claimed to have 275 Bipartisan bills that had passed the house prior to 2019, but been ignored by the Republican controlled senate.
FactCheck.org looked into this claim and found large numbers had fewer than 10 republican votes.
H.R. 1644, Save the Internet Act: 1 yea, 190 nays.
H.R. 2722, SAFE Act: 1 yea, 184 nays.
H.R. 582, Raise the Wage Act: 3 yeas, 192 nays.
H.R. 9, Climate Action Now: 3 yeas, 190 nays.
H.R. 7, Paycheck Fairness Act: 7 yeas, 187 nays.
H.R. 6, American Dream and Promise Act: 7 yeas, 187 nays.
H.R. 8, Bipartisan Background Checks Act: 8 yeas, 188 nays.
H.R. 5, Equality Act: 8 yeas, 173 nays.
H.R. 397, Rehabilitation for Multiemployer Pensions Act (Butch Lewis Act): 29 yeas, 168 nays.
H.R. 1585, Violence Against Women Reauthorization Act: 33 yeas, 157 nays.
Pelosi's office clarified the single vote requirement when questioned by FactCheck.
When asked about the “bipartisan bills,” Pelosi’s office sent us a list of 283 “bipartisan bills” with this explanation: “A bill is considered bipartisan if it received at least one Republican vote on the House floor or if it has at least one Republican cosponsor and was passed by voice vote.”
And to be clear this is not a Democrat only issue. The linked article cites similar language from the House leader in 2014. Republican John Boehner.
In 2014, for example, then-House Speaker John Boehner boasted that “almost all” of the 46 “jobs bills” awaiting action in the Senate “passed the House on a bipartisan basis.” But, as we wrote at the time, half of those bills had fewer than 20 Democratic votes each, including two that received no Democratic votes and 12 others that got 10 or fewer votes each from the opposing party.
Any political move which is widely supported by the majority of both parties, is considered a bipartisan act.
The simple definition to the term "bipartisan" is "of 2 parties", that's all. The common use of this term, is when the issue is supported by the 2 "Parties", not even referring to individual persons of the party (see Merriam-Webster's definition).
However, some people can opt to use this term when there are a significant amount of people of the other party participating in the act. But when there are hardly a few, the use of this term seems like an appeal for undeserved credibility (I don't deny the obvious facts mentioned by Jontia)
Merriam-Webster defines bipartisan as "marked by or involving cooperation, agreement, and compromise between two major political parties". So a bipartisan bill is a bill where neither party has the required votes on its own (because some members of the majority party vote against the bill, or because the upper and lower house have a different majority party), but where the two parties together do have enough supporters of that bill to get it passed. Note that in case the upper and lower house have a different majority, every bill that passes both houses is by (this) definition bipartisan, but some bills that fail to pass both houses might still have passed one of the houses with bipartisan support.
If one of the parties has the numbers to push a bill through on its own, but a few members of the other party also vote for that bill, that's not typically considered bipartisan because such a bill required no compromise or cooperation with the other party. In the extreme case where almost everyone votes for a bill, that's most often called wide support and not usually described as bipartisan support either for the same reason (unless a serious effort has been done to get both parties on board, often for a symbolic reason).
Note that Merriam-Webster also includes the wider definition of "of, relating to, or involving members of two parties" which allows politicians to claim bipartisan support whenever any politician of another party is involved in a bill. But that's not the way people typically use the term.
Here the term "bipartisan support" has several senses:
Aggregate bipartisan congressional support. The two dominant parties, taken as a whole, mostly agree to support or not support some bill, law, rule, action, or principle.
Bilateral bipartisan congressional support. Each of the two dominant parties, taken separately, and as a whole, mostly agree to support or not support some bill, law, rule, action, or principle.
Aggregate bipartisan public support. Any statistical majority of voters from the two dominant parties mostly agree to support or not support some person, group, action, or system.
Bilateral bipartisan public support. A statistical majority of voters from the two dominant parties, taken separately, and as a whole, mostly agree to support or not support some person, group, action, or system.
These four things are not the same. For example, in 2021 USA there is aggregate bipartisan public support for a $15 minimum wage; but there is not yet bilateral bipartisan congressional support. Or to the contrary, Congress might have bilateral bipartisan support for some military action which the aggregate public does not support.
The term bipartisan is often used equivocally, to suggest the likelihood of one kind of (missing) support, when only some other kind is truly present.
Since the United States has a two party system, "bipartisan support" requires "Yea" votes from members of both parties in order to qualify as bipartisan. It only takes one vote. For instance, in the recent vote on HR-1, the so called "For the People" bill, if one Republican had joined the Democrats in voting for the bill, it would have been considered a bipartisan bill.
Because the US has more than two parties, a bill could qualify as bipartisan if members of parties vote for a bill that normally caucus with one of the two dominant parties. Bernie Sanders (I-VT) would qualify as a vote from the Democrat party, as an example.