That's a good one.
Unfortunately unlike MSSQL, ASE does not record anywhere in its MDAs the size of the dump - or percentage of its progress.
I guess the only way to find it out is - yes - "grepping" the backup server log messages or using du variations - if you run on Unix/Linux. You may findstr/dir on windows too, but as folks indicate here the only method as of today is scripting (+/- xp_cmdshell where possible).