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While a single bank transfer from a jointly-held account may be acceptable, it is still probably better practice to at least have separate deposits made, and ideally from separate bank accounts.  It makes substantiation much easier when they are separate, payments, and can eliminate the need for filing two Gift Tax Returns (one for each spouse, since there is no "joint Gift Tax Return") if otherwise neither would be necessary.

The reason why is that if any individual makes a gift that is greater than $15,000 (whether or not the gift is a one-time gift or the cumulative value of all gifts throughout the year), then Form 709 (Gift Tax), must be filed.  As mentioned before, married couples must file separate gift tax returns, but, also mentioned before, each spouse can gift up to the $15,000 limit on individual gifts.  Married couples may also choose to split any gifts that they make from jointly-held property, but this requires separate Gift Tax Returns to be filed, regardless of the gift amount.  

It is a complex subject, and more information can be found at the following link: Instructions for Form 709.  Here are a couple of excerpts from that webpage.  First, note the following (other than the subheadings, bolding is added):

Who Must File

In general. If you are a citizen or resident of the United States, you must file a gift tax return (whether or not any tax is ultimately due) in the following situations.

• If you gave gifts to someone in 2019 totaling more than $15,000 (other than to your spouse), you probably must file Form 709. But see Transfers Not Subject to the Gift Tax and Gifts to Your Spouse, later, for more information on specific gifts that are not taxable.

• Certain gifts, called future interests, are not subject to the $15,000 annual exclusion and you must file Form 709 even if the gift was under $15,000. See Annual Exclusion, later.

• Spouses may not file a joint gift tax return. Each individual is responsible for his or her own Form 709.

• You must file a gift tax return to split gifts with your spouse (regardless of their amount) as described in Part 1—General Information, later.

• If a gift is of community property, it is considered made one-half by each spouse. For example, a gift of $100,000 of community property is considered a gift of $50,000 made by each spouse, and each spouse must file a gift tax return.

• Likewise, each spouse must file a gift tax return if they have made a gift of property held by them as joint tenants or tenants by the entirety.

• Only individuals are required to file gift tax returns. If a trust, estate, partnership, or corporation makes a gift, the individual beneficiaries, partners, or stockholders are considered donors and may be liable for the gift and GST taxes.

• The donor is responsible for paying the gift tax. However, if the donor does not pay the tax, the person receiving the gift may have to pay the tax.

• If a donor dies before filing a return, the donor's executor must file the return.

As noted above, any type of jointly-held marital property that is split between the spouses to gift requires two separate Gift Tax Returns, one for each spouse.  In addition, note these further comments:  

Lines 12–18. Split Gifts

A married couple may not file a joint gift tax return. However, if after reading the instructions below, you and your spouse agree to split your gifts, you should file both of your individual gift tax returns together (that is, in the same envelope) to help the IRS process the returns and to avoid correspondence from the IRS.

If you and your spouse both consent, all gifts (including gifts of property held with your spouse as joint tenants or tenants by the entirety) either of you makes to third parties during the calendar year will be considered as made one-half by each of you if all of the following apply.

• You and your spouse were married to one another at the time of the gift.

• If divorced or widowed after the gift, you did not remarry during the rest of the calendar year.

• Neither of you was a nonresident not a citizen of the United States at the time of the gift.

• You did not give your spouse a general power of appointment over the property interest transferred.

If you transferred property partly to your spouse and partly to third parties, you can only split the gifts if the interest transferred to the third parties is ascertainable at the time of the gift.

The consent is effective for the entire calendar year; therefore, all gifts made by both you and your spouse to third parties during the calendar year (while you were married) must be split.

If the consent is effective, the liability for the entire gift tax of each spouse is joint and several.

If you meet these requirements and want your gifts to be considered made one-half by you and one-half by your spouse, check the "Yes" box on line 12, complete lines 13 through 17, and have your spouse sign the consent on line 18.

If you are not married or do not wish to split gifts, skip to line 19.

The above is a bit complicated because this information is what is required (among other information) for a married couple to make the election.  Thus, unless the couple lives in a community-property state (where the election will be forced and they have no choice but to file two separate Gift Tax returns), a married couple can avoid all of this filing by making separate gifts within the limits.