This question of passing during nidda bothered me many years ago when our first child was born. The answer lies in the nature and the history of the custom for couples not to hand things to each other when the wife is nidda. The sages of the Talmud did not legislate it, and if you think about it, if they had, they would have had to extend the prohibition to other forbidden relations. If one is allowed to be secluded with his nidda-wife but may not directly pass her objects lest he it lead to touch which may lead to intimacy, then how much more so must he not directly pass objects to women with whom he is not allowed to be secluded! Also, the very prohibition would be an “enactment over an enactment:” Passing might first lead to accidental touch, which itself is not a sin. The law as laid down by the Talmud is as codified by Maimonides (Forbidden Relations, 11:19) who does not mention this prohibition.
For millennia, Jews did not consider the idea that the couple handing each other keys or cucumbers during the nidda times could lead to anything else. The first to actually refrain from such behavior was none other than Rashi, who adopted this stricture upon himself (Tos. to K’thubboth 61a). Like many strictures of his era, it spread rapidly throughout the world, and even earned mention in the Shulhan Aruch despite the fact that most Rishonim, including the Rif and Maimonides, had never heard of it, and others, like the Tosafists, rejected it as halacha. I would like to claim that the Beth Yosef’s language in Yoreh Deah 195:2 is also not a prohibition, but rather good advice, “He should not touch her, even on her pinkie, and he should not hand anything to her hand, nor accept anything form her, lest he touch her flesh,” although it is clear from the next line that the Rema did consider this a matter of straight prohibition: “So too, throwing from his hand to her hand or the opposite is also prohibited.” Since then, you can not find any Orthodox halachic work that does not disagree with that formulation.
However, If you check the Pithhei T’shuva (ad loc., 3) you will find that with regard to passing the baby, there is room for leniency. While the halachic concept invoked, “a living being carries itself,” does not seem relevant because the issue is incidental contact between the spouses and not the manner of carrying the baby, we see that this custom of not passing during nidda is not so strong as to require even pressing circumstances in order to be put aside when it may result in an inconvenience.
It is now with great trepidation that I give my own opinion concerning something that those in your situation often find themselves having to do: putting the baby down momentarily on a table or chair, or on a seat on a moving bus, instead of directly into someone else’s arms. Doing so, especially on a moving bus, is outrightly prohibited by Torah law, as it endangers the child, and just because you are her parents, it does not give you the right to endanger her because you wish to act strictly with regard to this custom.
Further, even if there is someone else who can act as a go-between to take the child from your arms and give her to your wife, it is unwise to make use of him or her because 1. he or she will by force have to be of the opposite sex of one of you, and is therefore risking inappropriate incidental contact with the problematic one of you, and 2. because your unnatural actions will broadcast to everyone that you are observing your nidda separation. Therefore, when dealing with the baby, you must hand her directly to your wife, and she must hand her directly to you, unless you are both 1. alone and 2. have an actual safe place to put her, like her motionless and guard-railed crib, or alternatively, you are only in the presence of family who are already in the know about your situation and have no problem contacting either of you, e.g. in your mother’s presence, as she knows that your wife recently gave birth and she has no issues with regards to coming into contact with either of you.
In short, when traveling, safety first. Do not ever put the baby in danger. At home, if you find keeping nidda difficult, you should maybe even adopt more restrictions in oder to keep your distance from each other.