The greater New York City area is the top fundraising region in the country and federal candidates from all over the country make the trip to New York for fundraising events and to have personal contacts with major donors.
Bloomberg is sending a personal letter to major Democratic donors asking them to not contribute to certain Senators who voted in April against a bill for more background checks on those buying guns. While most Democratic donors will contribute to whomever they want, the donors attending fundraising New York events could easily ask pointed questions of candidates about gun control.
The release and publicity of the objectives of the letter to the New York Times also serves as a warning to the U.S. Senate Democratic leadership that they should be corralling Democratic senators to vote together as a party that stands for stronger gun control. The leadership will easily get the message since anything that reduces fundraising for Democratic U.S. Senate candidates could affect elections that are vital to maintaining their slim majority in the Senate.
In some ways the letter to donors is a good tactic since it adds many others to a lobbying effort on a particular issue, but in other ways it utilizes an economic elite to lobby candidates with the use of money.