Is it appropriate to omit "to" after "ought"?

It's not typical.

The American Heritage Dictionary entry for ought has the following usage note:

Unlike other auxiliary verbs, ought usually takes to with its accompanying verb: We ought to go. Sometimes the accompanying verb is dropped if the meaning is clear: Should we begin soon? Yes, we ought to. In questions and negative sentences, especially those with contractions, to is also sometimes omitted: Oughtn't we be going soon? This omission of to, however, is not common in written English.

The omission of to is more frequent in American English. Quirk & al. (A Grammar of Contemporary English) say:

Ought regularly has the to-infinitive, but AmE occasionally has the bare infinitive in negative sentences and in questions (although should is commoner in both cases):
- You oughtn't smoke so much.
- Ought you smoke so much?