To write or to write to?

Write is a verb that can be used as a transfer (3-place) verb, and thus can have an indirect object, marked with to.

1. She wrote a long letter to Bill.

This can participate in the Dative Alternation, which drops the to and reverses the order:

2. She wrote Bill a long letter.

Write in this usage also allows the direct object to be understood as some kind of letter or message, since that's what the usage specifies. This leaves only the indirect object.

But the deletion of the predictable direct object can occur with either variant.

(1) above produces (3) below

3. She wrote ____ to Bill.

while (2) above produces (4) below.

4. She wrote Bill ____ .

So they're both correct, and identical, because syntactic alternations don't change meaning.

The practice in British English is to use write to when there is no direct object, so we would say I wrote to your uncle, rather than I wrote your uncle. However, when a direct object is present and it occurs after the name of the person addressed, to is omitted, so we would say I wrote your uncle a letter. If the direct object occurs directly after the verb, to reappears: I wrote a letter to your uncle.