No, you can't write the spells you know as a Bard into your spellbook.
There are 2 ways (outside of levelling as a Wizard) that a Wizard can add spells to their spellbook. The first is by finding them:
When you find a wizard spell
of 1st level or higher, you can add it to your spellbook if it is of
a spell level you can prepare and if you can spare the time to
decipher and copy it.
What does it mean to "find" a spell? Some examples are given immediately preceding this:
You might find other spells during your
adventures. You could discover a spell recorded on a scroll in
an evil wizard’s chest, for example, or in a dusty tome in an
While this is not meant to be an exhaustive list, it's strongly suggestive that finding a spell means finding it written down. It certainly doesn't suggest that knowing it is the same as finding it.
The second method for Wizards to add spells to their spellbook is from their prepared spells.
If you lose your spellbook, you can use the same procedure
to transcribe the spells that you have prepared into a new
You don't prepare your Bard spells, so this method won't work either. Note that even if you did prepare Bard spells:
So even if you did prepare Bard spells, they wouldn't be considered to be prepared by the Wizard class and wouldn't be usable with Wizard class features, including scribing.
With all that said, you should be able to craft a spell scroll of Comprehend Languages as a Bard (Crafting a Magic Item, DMG pg. 128) and then copy it into your spellbook from there.
A wizard spell on a spell scroll can be copied just as spells in spellbooks can be copied.
However, both the rules on finding spells and the rules on spell scrolls agree that the spell must be a "wizard spell". Unfortunately, the rules never define what it means for a spell to be a wizard spell, or a bard spell, or any other class's spell. The best evidence I can find is this:
Each time you gain a wizard level, you can add two
wizard spells of your choice to your spellbook for free.
The only interpretation I can come up with of this that makes any sense is that wizard spells just means spells on the wizard list. This would mean that spells common to both the can be scribed by a Bard and then copied by a Wizard.
This strategy is reliant on some ambiguous points, and requires explicit DM permission, since it's up to them whether you can craft items or not. There are also additional conditions to copying spell scrolls written in the DMG entry for spell scrolls.