u/sunagainstgold has written some previous answers about the problem of English vernacular Bibles in the 15th century, see:

In the 4th century, Jerome translated the Bible from Greek into Latin. It took until the 16th century for Luther to translate the Bible from Latin into German. So why did the Catholic Church decide to stop translating the Bible?

and Was it illegal for laypeople to own a Bible in the Middle Ages?

Hopefully those help, and maybe she or someone else can comment on the political risk to Henry IV specifically.

Henry could be justifiably confident that he would face no religious, political, or, er, biological consequences for owning an English-language Bible. Also, he was instrumental in ensuring that owning an English-language Bible was evidence that could get someone burned at the stake.

First, it's important to point out why English Bibles, not just Bibles in England, posed such a danger. By the late Middle Ages, literacy rates were rising among lay people--but they were rising primarily in the vernaculars. Latin was associated strongly with the Church (even though urban grammar schools were increasing in number). So the popular assumption was that vernacular = lay; Latin = clergy. English Bibles were accessible to anyone who could read or listen to anyone who could--priests could not control it.

This was not usually a big deal! Throughout the Middle Ages, the western Church as a whole had no rule against ownership of vernacular (non-Latin) Bibles. Indeed, while English Bibles were such risky possession in 15th century England, some German and Dutch Bible owners were taking their texts with them to Mass or sermons to follow along. In the late 15th century, the Archbishop of Mainz (Germany) declared that any new translations of the Bible into German needed to get his approval first. Yeah...the three German Bible versions between then and Luther didn't bother to seek approval, and there was no provision against purchasing them.

What the Church opposed wasn't lay people reading scripture; it was lay people interpreting it. The danger was that they might come up with something that contradicted the Church's official doctrine. Especially with respect to the Church/clergy's authority. And starting in late 14C England, a semi-organized movement known as the Lollards was making a push for just that.

Without getting into a complicated historiographical mess over the extent to which "Lollards" constituted a formal group: Lollard beliefs included:

• rejection of major sacraments (Church rituals mandatory for all believers, and used in some ways for religious control)
• denial that in the sacrament called the Eucharist, wafers and wine became the actual body and blood of Christ (a transformation that only a priest could make)
• rejection of pilgrimages, papal pardons, images of the saints, pretty much the saints, prayers for the dead (things that in various ways were huge money- and power-draws for the church)
• and, oh yeah: the sole authority of Scripture as the source of religious, and belief that everyone should be reading it and talking about correct interpretations for themselves

The growing presence of Lollardy from the late 14C into the earliest years of the 15C did not trigger an immediate condemnation of English Bibles. In fact, clerical writers like Richard Ullerston, who was emphatically not a Lollard, were still defending the importance of firsthand access to scripture for lay people. They just argued that it needed to be mediated by a priest's guidelines, whether in sermons or other literature.

But fear among clerics was growing of the threat posed by Lollardy to the authority of the Church, in the broader sense of Lollardy as a heresy. So in 1405, Henry issued a judgment that heretics could be burned at the stake. Then the English Bible became the focus. In shorthand knowledge, it was banned in the Constitutions of 1409, and possession of it could be a death sentence.

That's the background. Now let's talk about reasons Henry wasn't in any danger. The most important being: the Constitutions did not actually ban English Bibles.

There were multiple different translations of the Bible into English by 1409. The one that most concerned the Church is known as the Wycliffite Bible, after the priest/Oxford professor (John Wyclif) who is credited with developing the theology associated with the Lollards. He was originally thought to have been its translator, although scholars no longer agree with that particular point. This Bible, the Church banned ownership of. They also banned subsequent translations that, they feared, might have various translated verses or marginalia with Lollard-tainted perspectives.

However, earlier translations were a (slightly) different story. Lay owners of pre-Wyclif scripture in English were required to turn them over to their priest--for inspection, not destruction. So all that someone in possession of an English Bible would have to do, if caught, was to claim theirs was an older version.

Henry was not in danger for a second key reason: he was rich. (Okay, he was also king, but this applied to more than just the king.) Owning a Wycliffite or later English Bible was evidence of heresy. But it did not constitute proof on its own. Vernacular Bible owners who burned at the stake did so because it was one piece of evidence among many. This attitude went hand-in-hand with allowing flexibility in the enforcement of De heretico comburendo, that pesky 1401 law of Henry's that...well, it doesn't take Latin to recognize "heretic" and "burn" (combust) in there.

And as scholars have shown, the actual use of De heretico comburendo combined with the 1407 Constitutions disproportionately targeted the urban bourgeoisie/lower middle class. While there are always exceptions, the nobility and gentry could generally count themselves as safe, in significant part because Church leaders figured they were safe--safe in the sense of not wanting to overturn a socio-religious structure that was quite beneficial to them.

So if you wanted to own a vernacular Bible in 15th century Europe, it was a far better idea to own it in Germany, the Low Countries, Italy, or France than in England, yes. But while ownership of Bibles in English was evidence that helped send people to burn to horrific death, that death sentence was by no means automatic.

Sometimes it's good to be king.