When we read the seminal essay of "sense and reference" by Frege, one of the most important ambiguity is the meaning of "bedeutung". Of course Michael Dummett the Late great philosopher point out to this difficulty in his books but I think its not clear and unambiguous.. I think that all in all we can mention two meaning for bedeutung: first is the referent or something which is referred by expression. Second is the way in which the action of reference described..but I can't say that which meaning was aimed by Frege...
This is not an easy question. The first problem is that the German ‘bedeuten’ means something like ‘mean’ or ‘signify’ or ‘indicate’, which led to the translators changing the translation from ‘reference’ in the original edition to ‘Meaning’. Thus ‘sense and Meaning’, not ‘sense and reference’. This was controversial. The second is that Frege seems to have changed his mind about ‘Bedeutung’ as his views progressed. Originally he held something like a ‘direct reference’ view of the sentence. Thus ‘John is tall’, on his original view, contains the object word ‘John’, which refers to John himself, and ‘is tall’ refers to the concept ‘is tall’. Thus what is signified by the sentence is the complex entity
John himself is a component of the meaning (bedeutung) of the sentence. Later he realised that this view is absurd. How can a mountain such as Mont Blanc, with all its snowfields, be part of the meaning of a piece of language? So he revised his view to include ‘sense’ or ‘Sinn’, so that the sense is something more like the meaning, whereas the Bedeutung is the object meant.
I suggest reading the early chapters of Gareth Evans’s The Varieties of Reference which outline the problem of exegesis in some detail. Also recommended is The Frege Reader by Michael Beaney.
Caveat, I am writing this from memory. It is some years since I looked at Frege.