That is true, however Heb 9:12 still has Christ's blood as being more proficient than both the blood of bulls and goats. The book of Hebrews deals with Christ's superiority to the High Priest in sinlessness earlier on and still highlights Christ's blood being more powerful than that of bulls to enter into the sanctuary. (cf. Heb 4:14-5:10, 7:1-8:13)
Yes, since it is a comparison to the earthly it still holds true, to show it superior. But Jesus woudn't need to fulfill that directly.
Also more than one service involved entry into the sanctuary, and more than one involved bulls.
Lev 4:13 "If the whole congregation of Israel sins unintentionally and the thing is hidden from the eyes of the assembly, and they do any one of the things that by the LORD's commandments ought not to be done, and they realize their guilt,
Lev 4:14 when the sin which they have committed becomes known, the assembly shall offer a bull from the herd for a sin offering and bring it in front of the tent of meeting.
Lev 4:15 And the elders of the congregation shall lay their hands on the head of the bull before the LORD, and the bull shall be killed before the LORD.
Lev 4:16 Then the anointed priest shall bring some of the blood of the bull into the tent of meeting,
Lev 4:17 and the priest shall dip his finger in the blood and sprinkle it seven times before the LORD in front of the veil.
The sin offering for the whole congregation demanded that bull blood be brought in.
While the details show that Jesus fulfilled the entry and cleansing of the Day of Atonement in Hebrews 9-10, it also shows that he fulfilled other services as entries as well, and that is why He entered once, fulfilling all the entries according to verse 12.
It is unlikely that the sin offering for the congregation was in mind here though because it says He entered "by means of" blood. Blood was not required to enter the first compartment, as the priests had daily access to it for various tasks. But blood was required to enter in on the Day of Atonement.
So likely your thought on that is accurate, it is merely a comparison to the earthly, showing Jesus' superiority.
One other service, the inauguration, MAY have included taking in Blood from bulls.
Number 7-8 shows that bulls were part of the sacrifices for dedicating the altar and anointing the priests. It does not indicate blood was taken into the sanctuary.
Ex 40:9, also on the inauguration, indicates that oil was taken into the sanctuary to anoint it, but Josephus indicates blood was too
The same he did to the tabernacle, and the vessels thereto belonging, both with oil first incensed, as I said, and with the blood of bulls and of rams, slain day by day one, according to its kind
Ant. III. 8, 6. http://www.sacred-texts.com/jud/josephus/ant-3.htm
This seems to be affirmed by Hebrews, though the type of blood is not specified:
Heb 9:21 And in the same way he sprinkled with the blood both the tent and all the vessels used in worship.
Incidentally Adventist scholar Richard Davidson argues that 9:12 is referencing the inauguration, not the Day of Atonement, based on the particular word used for "goat" which is only used in that service.
However, even he is compelled to acknowledge that 9:25 references the Day of Atonement.
I would say both the DOA and inauguration (and the sin offering of the whole congregation) are in view in 9:12 because Jesus entered once, fulfilling all the entries.