#Bards can scribe scrolls

Xanathar's Guide to Everything lays out the requirements to scribe a scroll as follows:

> the character must have proficiency in the Arcana skill and must
> provide any material components required for the casting of the spell.
> Moreover, the character must have the spell prepared, or it must be
> among the character’s known spells, in order to scribe a scroll of
> that spell.

Beyond this, there are no requirements.

###Your DM must allow magical item creation and downtime must be used

A spell scroll is a magic item and thus falls under the rules for creating magic items. The rules for creating magical items are optional and must be allowed by your DM before they can be used. So talk to them.

Also note that the rules for scroll scribing in XGtE specifies that scroll scribing is a downtime activity. So they would use the downtime rules. Consult your DM to see how they want that to work as well.