To OP, this is F30 subforum, your questions maybe better addressed in E90 subforum.

In general if there is coolant loss to the extent that engine can overheat, one prudent option will be to tow car to shop instead of driving.

 

The 2004 model year 3 Series was the E46 platform, not the E90 (let alone F30). Meanwhile, until a moderator comes along to move your post, how about giving us some useful information: Which BMW exactly? Don't try to use jargon when you're unsure; the model designation from the trunk--or better still, from the plate on the driver's door jamb--is sufficient. A wider-angle photo to give us some context will be helpful, too.

Assuming this really is an E46, that is probably an M54 engine and you absolutely MUST NOT drive it like this. Overheating an aluminum-block engine is the kiss of death--as in, buy-another-engine-it's-the-cheapest-fix death.

I'll have more to say about that hose once I am sure exactly which engine and hose I'm seeing.

 

Common failure point on motors. Take your pic, go to dealer, (It's a cheap part) and get replacement. The E90 was not made until 2006 but you list your car as a 2004. Again, run the VIN and get the right part.

 

I agree that the car is an E90 and thus has an N52 (and not an E46 with an M54). Therefore, the part is likely PN 11537545890, "Hose, cylinder head-thermostat".
Looks like it's about $32 (Rein) to $75 (Genuine BMW) depending on where you get it.

As others have said, do not drive the car until this part is replaced and the cooling system is bled. If you cannot replace this part yourself, call a tow truck and have it hauled to the shop on a flatbed.

 

I agree that the car is an E90 and thus has an N52 (and not an E46 with an M54).

I found another thread by OP with additional photos--agreed, that engine is an N52 not an M54. Model year of the car must be wrong (unless OP is outside the US).

 

Thanks for the update. I moved this to the E90 forum.

 

See realoem.com for the part number. Aluminum replacements are available as an alternative to the OEM plastic part.
And yeah, don't try driving it.

Sent from my SM-A102U using Tapatalk

 

Upgrade to aluminum, confirm fitment first.

BMW Aluminum Coolant Hose Flange - Rein CHC0609

BMW Aluminum Coolant Hose Flange - Rein CHC0609

www.fcpeuro.com