I suspect that the BAM datasets is close to or over 2 GB in size. For data of this size, use the FTP method of upload (instead of local file browsing). Instructions for Galaxy upload.
If the file is less than 2 GB, the speed of your internet connection could be a factor. Try FTP for this case as well as a first pass solution.
These are true on any Galaxy server. It is possible for a local Galaxy to display upload problems due to other reasons, but this is where to start. Send more details if it does not work. Best, Jen, Galaxy team
ps: IGV was included as a tag. Is this related to the Galaxy upload issue? Or just what you plan to do (visualize in IGV) once the data is loaded into Galaxy?